BI Grade 7: Chapters 1-4
x ≤ 40
A number is at most 40.
x ≥ -18
A number is great∧er than or equal to -18
x < 4
A number is less than 4.
35x + 55 = 160
A plumber charges $55 for a service call plus $35 per hour. The plumber's total bill was $160.
Infinitely Many Solutions
An inequality has _________.
14(3a + b)
Factor the expression: 42a + 14b
4(y − 5)
Factor the expression: 4y − 20
2.5(2 + q)
Factor the expression: 5 + 2.5q
−2x − 3
Find the difference: (x − 1) − (3x + 2)
x+x+2+x+4=72
Find three consecutive even integers whose sum is 72
17/20
0.85
x+x+2=-88
1) Find two consecutive odd integers whose sum is -88.
x = 0
1+ 4(2x + 1) = 5
5.5
1.8 − (−3.7)
0.1
1/10
None of them
How many months have 32 days?
Infinitely Many Solutions
How many solutions? 5(x + 2) - 3x = 2(x + 5)
No Solution
How many solutions? -2(x + 1) = -2x + 5
2.5w and 4w
Identify the like terms in the expression: 2.5w − 3y + 4w
x = 22
1/2x = 11
x = 14
1/2x = 7
x = 27
1/3 x + 2 = 11
1/4
1/8 divided by 1/2
0.17
18 eggs cost $3.06. What is the cost per egg?
x ≤ 2
18 ≥ 5x + 4x
4x - 2
2(2x - 1)
x = 7
2(3x + 1) = 7x - 5
8x + 14
2(4x + 7)
10x - 18
2(5x - 9)
14x - 6
2(7x - 3)
x = -1
2(x + 2) = 2
x = 9
2/3x = 6
x = 12
2/3x = 8
0.4
2/5
x = 27
20 = x - 7
50
20/x = 6/15
x ≥ -6
20x ≥ -120
35
25/x = 10/14
x = 5
2x + 10 = 20
x = -8
2x + 15 = -1
x≥ -7
2x + 6≥ -8
x = -13
2x + 9 = x - 4
x ≤ -2
2x - 4 ≤ -8
x = 7
2x - 6 = 8
6x - 9
3(2x - 3)
12x + 21
3(4x + 7 )
0.15
3/20
1 1/2
3/4 + 3/4
x = 16
3/4 x - 2 = 10
x = 32
3/4x = 24
x = -1
3x + 2 = -1
x > 4
3x + 4 > 16
x = 5
3x - 2= 13
x = 10
3x - 30 = 0
4x - 12
4(x - 3)
4x - 32
4(x - 8)
10x + 15
5(2x + 3)
x = 1/3
6x - 4 = -2
x = 10
6x - 8 = 52
x = -7
6x = -42
x = -1
6x = -6
x = 1
6x = 6
11
7 + (−1) + 12 − 7
$360
8 hockey sticks are $240. How much are 12?
x = -9
9x - 4 = -85
z and 4z
Identify the like terms in the expression: z + 8 − 4z
5
If 3 twinkies cost $1, how much is it for 15 twinkies?
8 miles
If Sally swims 2 miles in 1/4 of an hour, how many miles can she swim in an hour?
inverse of division
Multiplication
−9w − 55.8
Simplify the expression: 9(−3w − 6.2 + 2w)
m = (y - b)/x
Slope Intercept Form y = mx + b Solve for m
b = -a/m
Slope of a line in standard form is: m= -a/b Solve for b
b₁ = 2A/h - b₂
Solve for b A = ½(b₁ + b₂)h
b = 2A/h
Solve for b A = ½bh
h = 2A/(b₁ + b₂)
Solve for h A = ½(b₁ + b₂)h
h = 2A/b
Solve for h A = ½bh
k = 0.75
Solve the proportion.
x = (C - By)/A
Standard Form Ax + By = C Solve for x
inverse of addition
Subtraction
π = SA/(4r³)
Surface Area of a Sphere SA= 4πr³ Solve for π
67.5
The scale of a model train Is 1 inch to 13.5 feet. One of the cars of the model trains is 5 inches long. What is the length in feet of the actual train car?
31
The temperature in Juneau, Alaska was 13°F, while the temperature in Fairbanks, Alaska was -18°F. How many degrees warmer was it in Juneau than in Fairbanks?
K = 2
What is the constant of proportionality?
K = 3
What is the constant of proportionality?
K = 4
What is the constant of proportionality?
k = 10
What is the constant of proportionality?
k = 16
What is the constant of proportionality?
k = 20
What is the constant of proportionality?
-19
What is the opposite of 19?
18
What is the value of I -18 I ?
76
What is the value of I -76 I ?
8
What is the value of I -8 I ?
The Greeks
When Ms. Bixby taught sixth grade, what team was she on?
Natick
Which town do you go to school in?
7m + 19
While catching fireflies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fireflies and your friend has (4m + 6) fireflies. How many total fireflies do you and your friend catch?
You
While catching fireflies, you and a friend decide to have a competition. After m minutes, you have (3m + 13) fireflies and your friend has (4m + 6) fireflies. The competition lasts 3 minutes. Who has more fireflies?
Mr. Magarie and Ms. Trischitta
Who are the other two 7th grade math teachers at WMS?
Mrs. Doyle
Who is your L+L teacher this year?
Ms. Bixby
Who is your Math teacher this year?
Mr. Brennan
Who is your Science teacher this year?
Mr. Dumont
Who is your World Geo. teacher this year?
Mr. Gray
Who is your guidance counselor this year?
4 3/50
Write 4.06 as a fraction.
53/8
Write 6 5/8 as an improper fraction.
0.36
Write 9/25 as a decimal
x < 5
x - 1 < 4
3x + 8 = 2x - 17
x = -25
4x - 40 = 7(-2x + 2)
x = 3
x < 36
x/4 < 9
x = 14
x/7 - 4 = -2
1
x/7 = 3/21
x ≥ -135
x/9 ≥ -15
0.498
(- 0.2) × 8.3 × (- 0.3)
-7
(- 2.8) ÷ 0.4
-2.55
(- 5.1) × 0.5
2.22
(-11.1) × (- 0.2)
-70
(-42) ÷ (0.6)
-56
(-7)(8)
68.62
(-7.3)(-9.4)
x = 10
(1/2)x = 5
x = 15
(1/3)x = 5
x = 20
(1/4)x = 5
x= -45
(1/5)d = -9
x = 25
(1/5)x = 5
x = -18
(2/3)x = -12
x = -12
(2/3)x = -8
x = 18
(2/3)x = 12
x = 12
(2/3)x = 8
x < 15
(2/5)x - 4 < 2
0.5b + 7
(4 - 3.7b) - (-5.4b - 4) - (1.2b + 1)
56
(7)(8)
x ≥ 8
(x/2) - 1 ≥ 3
x = -27
(x/3) = -9
x = 27
(x/3) = 9
x = -24
(x/4) = -6
1/18
-1/2 - (-5/9)
56
-10 2/3(-5 1/4)
x = 5
-10(-4x + 7) = 130
-432.558
-102.99 x 4.2
10.20
-55.08 divided by -5.4
x = 3
-5x - 2 = -17
x = -11
-5x - 4 = 51
x = 48
-6 + x = 42
-1 9/20
-6 1/5 - (-4 3/4)
-1
-6 = 6p
-12x + 30
-6(2x - 5)
-6.505
-6.98 + 0.475
-152
-65-87
x = -3
-6x - 8 = 10
x = 7
-6x = -42
x = -2
-6x = 12
x = -9
-7 + x = -16
x = 23
-7 + x = 16
x ≤ 9
-7(x + 2) ≥ −77
161.28
-7.2(-22.4)
0.2
1/5
x = -8
245 = -5(4x - 17)
x = 3
27 = 8x + 3
x = -5
2x + 5 = -5
x = 4
2x - 4 = -4(x - 5)
0.096
3.2 × 0.3
15.5
3.4 − (−12.1)
x = 4
3/4x = 3
−4.3
5.4 + (−9.7)
2.7
9.8 − 7.1
$0.58
A pack of 6 Dr. Peppers cost $3.48. What is the unit price for 1 Dr. Pepper?
1.5x + 7 = 11.50
A pizza shop charges $7.00 for a pizza and $1.50 per topping. The total charge for Noah's pizza is $11.50.
3
A recipe for making 12 cupcakes requires 2 cups of flour. How many cups of flour would be needed to make 18 cupcakes?
8
A rectangular pool is twice as long as it is wide. What is the width of the pool if the perimeter is 48 yd?
4w + 16
A rectangular room is 10 feet longer than it is wide. How many 1-foot square tiles does it take to tile along the inside walls of the room?
22
A shop produces 39 wetsuits every 2 weeks. How many weeks will it take the shop to produce 429 wetsuits?
x/2+7=12
Abhasra spent half of her weekly allowance at the movies. To earn more money her parents let her clean the windows in the house for $7. What is her weekly allowance if she ended with $12?
Inverse of subtraction.
Addition
linear expression
An algebraic expression in which the exponent of each variable is 1.
187.5
An amusement park line is moving about 4 feet every 15 minutes. At this rate, approximately how long will it take for a person at the back of the 50- foot line to reach the front of the line?
50x + 10 = 128
Ben bought some $50 video games and one $10 movie. He spent $128.
C.
Benny earns $12.00 per hour as a lifeguard. He earns a bonus of $75.00 for taking a training course. Which graph best represents the number of hours must be work to earn at least $399.00?
57
Bill sold 38 papers in 2 hours. At this rate, how many papers would he sell in 3 hours?
5
Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months will it take for Bill to weigh the same as Phil?
352
Bobby drove 110 miles, and his car used up 5 gallons of gas. How many miles can he drive with 16 gallons of gas?
The Red Sox
Boston's baseball team.
The Celtics
Boston's basketball team.
The Bruins
Boston's hockey team.
0.6x + 18 = 36
Brady rents a paddle board. It costs $36 in total. There was an $18 rental fee and a $0.60 charger per hour.
55x + 35 = 160
Brooke spends $55 on each shirt she purchased and bought a pair of jeans for $35. Her total purchase was $160.
Unit Price
Cost per one unit/item.
63
Darrell drove 189 miles in 3 hours. What was Darrell's average rate of speed in miles per hour?
True
Determine whether the given value makes a true or false statement. 12 > f, if f = 3
True
Determine whether the given value makes a true or false statement. 16 < b + 8, if b = 22
False
Determine whether the given value makes a true or false statement. 3 > d, if d = 3
True
Determine whether the given value makes a true or false statement. 5r - 3 ≥ 25, if r = 6
Inverse of multiplication
Division
24=3x+18
Eugene had $24 to spend on three pencils. After buying them he had $18. How much did each pencil cost?
-9
Evaluate (-10) + (-2) + 3
2(b + 4)
Factor the expression: 2b + 8
12(3c + 2d)
Factor the expression: 36c + 24d
3.5(12 + h)
Factor the expression: 42 + 3.5h
6(n − 4)
Factor the expression: 6n − 24
12(6m − 5)
Factor the expression: 72m − 60
3(3 − 5x)
Factor the expression: 9 − 15x
−4(x − 9)
Factor the expression: −4x + 36
25x+612=912
Friendship's soccer team purchased uniforms and equipment for a total cost of $912. The equipment cost $612, and the uniforms cost $25 each. What equation can be used to represent the situation?
96
Gary can hike 2.5 miles in 30 minutes. At this rate, how long will it take him to hike 8 miles?
4x + 4500
Greenland has a population of "x" people. Barbados has a population of about 4500 more than 5 times the population of Greenland. Find the difference in the populations of these two countries
50 + 9.5x ≥ 300
Hayden earns $9.50 per hour as a lifeguard. He earns a bonus of $50.00 for taking a training course. How many hours must he work to earn at least $300.00?
additive inverses
Integers that are opposites are also called _________.
opposites
Integers that have the same absolute value but are located on opposite sides of zero are called _________.
r = I/(pt)
Interest formula I = prt solve for r
Yes
Is -3/2 a solution to x ≤ -9/5
No
Is 11 a solution to x < 8?
No
Is 15 a solution to x > 15?
Yes
Is 4/3 a solution to x ≤ 2?
The goal when solving an equation
Isolate the variable
12
It takes 20 minutes to cut a log into 5 equal-size pieces. How long will it take to cut a similar log into 3 equal-size pieces?
2022
Next year will be...
That all values in the solution set are LESS THAH the "given" value.
Shading in an arrow to the LEFT of a value on a number line represents...
That all values in the solution set are GREATER THAN than the "given" value.
Shading in and arrow to the RIGHT of a value on number line represents...
x = 3/2y + 3
Solve for x 2x - 3y = 6
x = 2/3y + 2
Solve for x 3x - 2y = 6
x = 7/2 - y
Solve for x 7 = 2(x + y)
x=c-b/a
Solve for x ax + b = c
x = ½y + 8
Solve for x y = 2(x - 8)
y = 2/3 x - 2
Solve for y 2x - 3y = 6
y = 3/2x - 3
Solve for y 3x - 2y = 6
y = (x + 4)/x
Solve for y x = xy -4
π = A/r²
Solve for π A = πr²
x = -10
Solve the equation. 3x + 5 = -25
x = 1
Solve the equation. 3x - 2/3 = 7/3
x = -3
Solve the equation. 6x - 2 = -20
Constant Of Proportionality
The constant ratio between two proportional quantities (usually simplified to whole numbers).
52.5n + 449.85
The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n + 29.99, where n is the number of different colors in the design. Write a simplified expression that represents the cost of 15 sweatshirts.
7
The sum of -25 and 32
75.6
The temperature of dry ice is −109.3°F. Th is is 184.9°F less than the outside temperature. What is the outside temperature?
t − 184.9 = −109.3
The temperature of dry ice is −109.3°F. Th is is 184.9°F less than the outside temperature. Write an equation to find the outside temperature.
715.36
The tickets to a LegoLand park cost $89.42 each. How much will 8 tickets cost?
8
There was a blizzard. Snow was falling at a rate of 4 ½ inches per hour. If the snow kept accumulating at the same rate, how long would it take for 3 feet of snow to accumulate?
72
Tia is painting her house. She paints 45 square feet in 2.5 hours. At this rate, how many square feet can she paint in 4 hours?
2.5x + 40 > 175
WRITE AN INEQUALITY Dennis is selling chocolate bars for a fundraiser, and if he sells over $175 worth of candy, he'll win a prize. If chocolates sell for $2.50 a bar, and Dennis has already sold $40 worth of candy, then how many more bars does he have to sell in order to win a prize?
7th
What grade are you in?
K = 1/2
What is the constant of proportionality?
K = 5/4
What is the constant of proportionality?
k = 200
What is the constant of proportionality?
k = 3/2
What is the constant of proportionality?
k = 40
What is the constant of proportionality?
k = 45
What is the constant of proportionality?
k = 46
What is the constant of proportionality?
k = 47
What is the constant of proportionality?
k = 6
What is the constant of proportionality?
k = 60
What is the constant of proportionality?
k = 750
What is the constant of proportionality?
k = 1/10
What is the constant of proportionality? 10y = x
k = 1/12
What is the constant of proportionality? 12y = x
k = 1/23
What is the constant of proportionality? 23y = x
k = 1/2
What is the constant of proportionality? 2y = x
k = 1/3
What is the constant of proportionality? 3y = x
k = 1/4
What is the constant of proportionality? 4y = x
k = 1/6
What is the constant of proportionality? 6y = x
k = 1/7
What is the constant of proportionality? 7y = x
Saturday
What is the day after Friday?
x < -5
What is the inequality for the graph?
KEEP THE SAME direction of the inequality symbol in the solution set.
Whenever we multiple or divide by a NEGATIVE on the OPPOSITE SIDE as the variable term we must....
REVERSE the direction of the inequality symbol in the solution set.
Whenever we multiple or divide by a NEGATIVE on the SAME SIDE as the variable term we must....
KEEP THE SAME direction of the inequality symbol in the solution set.
Whenever we multiple or divide by a POSITIVE on the OPPOSITE SIDE as the variable term we must....
KEEP THE SAME direction of the inequality symbol in the solution set.
Whenever we multiple or divide by a POSITIVE on the SAME SIDE as the variable term we must....
Lesley University
Where did Ms. Bixby go to GRADUATE school?
Roger Willams University
Where did Ms. Bixby go to UNDERGRAD college?
-20
Which integer describes 20 years ago?
1,500
Which integer describes ascending 1,500 feet?
-3
Which integer is the same distance from 0 as 3?
D.
Which of the following inequalities represents the phrase "three less than twice a number is at least negative one"? A. 2x + 3 ≥ -1 B. 3 - 2x ≥ -1 C. 3 - 2x ≤ -1 D. 2x - 3 ≥ -1
207
Which room is Mr. Brennan's?
206
Which room is Mr. Dumont's?
211
Which room is Mrs. Doyle's?
208
Which room is Ms. Bixby's?
Roger Williams University
Which school did Ms. Bixby attend for her UNDERGRADUATE degree?
Lesley University
Which school did Ms. Bixby earn her MASTERS degree from?
Roger Williams University
Which school did Ms. Bixby earn her UNDERGRADUATE degree from?
WMS
Which school do you attend?
Responsibility
Which team are you on this year?
Mr. Gray
Who is your guidance counselor?
Mr. Gray
Who is your guidance teacher this year?
Mrs. Doyle
Who is your language and literacy teacher this year?
Ms. Bixby
Who is your math teacher this year?
Mr. Brennan
Who is your science teacher this year?
Mr. Dumont
Who is your social studies teacher this year?
Mrs. D'Agostino
Who is your vice principal?
SpongeBob SquarePants
Who lives in a pineapple under the sea?
Spongebob Squarepants
Who lives in a pineapple under the sea?
28
William sold half of his comic book collection then purchased 10 more. He now has 24 comic books. How many books did William begin with?
0.85
Write 17/20 as a decimal.
8 17/50
Write 8.34 as a mixed number in simplest terms.
x > -1
Write and solve this inequality: Negative twelve times a number is less than twelve.
x ≤ 18
You can spend no more than $100 on a party you are hosting. The cost per guest is $4 and your budget for decorations is $28. What is the greatest number of guests that you can invite to the party?
x < 5.50
You can spend no more than $5.50.
x ≥ 19.75
You have at least $19.75 in your wallet.
8 - x ≤ 5
eight less a number is less than or equal to five
g = -72
g/-8 = 9
1
r - 3 = -2
24
r/4 = 6
x= -28
s/7 = -4
x + 3 < 12
the sum of a number and three is less than twelve
3x > -7
three times a number is more than negative seven
x < 7
x - 6 < 1
8x + 4 = 10 + 2x
x = 1
15x - 10 = -9x + 2
x = 1/2
42 + 7x = 8(x + 4)
x = 10
-14 - 3x = -5x + 8
x = 11
2x - 1 = x + 11
x = 12
8x - 16 = 4x + 40
x = 14
7x - 12 = 3 + 6x
x = 15
-8 - x = -4x +1
x = 3
-10x + 2 = -8x - 8
x = 5
9
(−3) + 5 + (−5) + 12
−5.19
(−4.79) + (−0.4)
0.8
(−8.1) − (−8.9)
-5.6
(−9.1) + 3.5
5x - 4
- (-5x + 4)
-3x + 2
- (3x - 2)
- 1/3 + (- 1/8)
- 11/24
2/3 + (-8/3)
- 2
x = -6
- 2x + 1 = 13
x = -5
- 3x + 7 = 22
- 2/3 + 2/9
- 4/9
1/4 + - 2/3
- 5/12
- 45.2 + (-9.3)
- 54.5
- 2 1/2 + (- 4 1/4)
- 6 3/4
- 3/4 + (- 1/8)
- 7/8
-33.3 + 25.25
- 8.05
-7.003
-0.003 + (-7)
1.09
-0.01 + 1.1
-6.66
-0.6 + (-6) + (-0.06)
-3.68
-0.7 + 0.02 + (-3)
x > -4
-1 - 6x - 6 > -11 - 7x
-182.608
-1.808 + (-180.8)
x = 13
-10x + 4 = -126
x = 19
-10x - 10 = -200
x = 11
-10x - 5 = -115
x = -10
-10x - 7 = 93
-5
-12 - (-7)
x = 1
-12x + 7 = -5
x = -17
-12x - 1= 203
x = 0
-13 = 4x - 13
x < 2
-13x > -26
x = 3
-15 = -5x
x ≥ 6
-15x ≤ -90
-11
-16 = y - 5
x ≤ 14
-16x ≥ -224
x = -5
-17 = 5x-7
- 2/25 + (- 15/25)
-17/25
x = -9
-18 = 2x
x = -23
-18 = x + 5
x = -13
-18 = x - 5
6x + 16
-2 (-3x - 8)
-14x + 6
-2 (7x - 3)
-2x + 14
-2 (x - 7)
x ≤ -6
-2 ≥ x + 4
6x + 16
-2(-3x - 8)
x > 11
-2(x - 7) < -8
x ≤ 22.5
-2(x - 7) ≥ -31
x ≤ 40
-2(x -5) ≥ −70
x = -27
-20 = x + 7
x = -13
-20 = x - 7
x = 10
-210 = -7(9x - 60)
11
-22.44/-2.04
-9
-26 - (-17)
x = 6
-2x + 16 = 4
x < 5
-2x + 4 > -6
x = 4
-2x - 3 = -11
21x + 18
-3 (-7x - 6)
x < 3
-3 - 6(4x + 6) > -111
21/22
-3 1/2 ÷ -3 2/3
12
-3 Times -4
21x + 18
-3(-7x - 6)
x < -10
-3(x + 2) > 24
-3.45
-3.1 + (-0.35)
x ≤ 4
-3x + 2 ≥ -10
x = -1
-3x + 5 = 8
x = -5
-3x + 7 = 22
x = -3
-3x - 11 = -2
x > -3
-3x - 4 < 5
x ≥ -9
-3x ≤27
-1 2/5
-4 1/5 x 1/3
-12 3/5
-4 1/5 ÷ 1/3
x = -24
-4 = x/6
x < -27
-4.5 > x/6
8.1
-4.86 ÷ (-0.6)
x = 6
-4x + 8 = -16
x = -4
-4x + 9 = 25
x = 16
-4x - 10 = -74
x = -15
-4x - 8 = 52
x = 14
-4x - 9 = -65
x ≥ -8
-4x ≤ 32
-13
-5 + (-8)
-13
-5 + -8
x = -1/3
-5 = 15x
x = -1/2
-5 = 4x - 3
-10x -35
-5(2x + 7)
-22.287
-5.7(3.91)
-1.83
-7.34 - (-5.51)
-2
-7m = 14
x = -6
-7x + 1= 43
x = 5
-7x = -35
x = -5
-7x = 35
0
-8 + 8
-18 13/24
-8 3/8 - 10 1/6
3.21
-8.49 + 11.7
x > 4
-8x + 19 < -13
x > -2
-8x + 2x - 16 < -5x + 7x
x = 20
-8x + 5 = -155
x > -2
-8x < 16
x ≥ -5
-9 ≤ x - 4
x = 36
6 + x = 42
x = 0
6 + x = 6
x ≤ -6
6 - 4(6x + 7) ≥ 122
36
6 posters cost $48. At that rate, how many posters can you buy for $288?
$120
6 t-shirts are $24. How much are 30?
2.02
6 − 3.98
12x + 18
6(2x + 3)
18x - 12
6(3x - 2)
x ≤ -4
6(x - 1) ≤ -30
-1.6
6.4 ÷ (-4)
1.425
6.84 ÷ 4.8
5
6/15 = 2/x
36
6/x = 2/12
6
6m = 36
All Real Numbers
6x + 2 - 6x < 14
x ≤ 7.5
6x - 18 ≤ 27
x = 11
6x - 5 = 61
17
100 students went on a field trip. 6 buses were filled and 10 students traveled to the destination in cars with their parents. How many students were on each bus?
x = 11
10x + 2 = 112
x = -13
10x + 7 = -123
16 + (-5)
11
- 3.52 + 14.7
11.18
-1/3
11/12 + (-7/12)
0.55
11/20
x = 17
11x + 10 = 197
x = -5
11x + 3 = -52
x = 7
11x + 6 = 83
x ≤ 7
11x ≤ 77
x = -23
7 + x = -16
x = 9
7 + x = 16
11
7 - (-4)
x = 10
7 - x = -3
4.2
7 − 2.8
x = -3
7(2 - x) - 5= 30
14x + 21
7(2x + 3)
5x + 14
7(x + 2) - 2x
2.3
3.1 + -0.8
x - 3.5 ≥ 12
3.5 less than a number "x" is greater than or equal to 12
x = 40
3/4x = 30
x = 8
3/4x = 6
0.6
3/5
x = 25
3/5x = 15
31
3/x = 6/62
7x - 14
7(x - 2)
x = 3
45 = 15x
x = -2
4x + 12 = 4
x = -1
4x + 16 = 12
x = 0
4x - 13 = -13
x < 1/2
4x - 2 < 0
x = -1/2
4x - 3 = -5
x = 12
4x - 4 = 44
x = -16
4x - 9 = -73
-20x + 5
5 (-4x + 1)
x ≥ 10
5 + 1/2x ≥ 10
x ≥ 1
5 + 2x - 3x(2 + 4) ≤ -x(3 + 5) -3
x = -5
5 + x = 0
x = 5
5 - 3x = -10
x = 1/3
5 = 15x
$1.80
5 apples cost $1. How much are 9?
-42
5 x (-8 2/5)
-20x + 5
5(-4x + 1)
x = 6
5(5 - x) = -5
x ≥ 6
5(6 + 3x) + 7 ≥ 127
x = 1
5(7x - 13) = -30
x = -5
5(n + 2) = 3n
x = 6
5(x + 2) = 40
5x - 25
5(x - 5)
x = -35
5(x - 6) = 3 + 8 (x + 9)
4.002
5.001 + (-0.999)
3.3
5.8 + (−2.5)
26
5/13 = 10/x
38
5/19 = 10/x
4 1/3 + (- 3 1/2)
5/6
0.625
5/8
-1/4
5/8 - (7/8)
19
5/x = 10/38
6
5s = 30
x = 2
5x + 1 = 11
x = 3
5x + 3 = 18
x = 4
5x - 7 = 13
x = -12
5x - 8 = -68
x < -18
5x < -90
x < 1
5x < 5
7x - 28
7(x - 4 )
x = 3
7(x - 4) = - 7
x ≥ 6.7
7.9 less than a number "x" is greater than or equal to -1.2
0.35
7/20
1.75
7/4
28
7/x = 2/8
x = 2
9x - 10 = 8
x < -5
9x - 13 < -58
x ≤ 8
A 15-passenger van is rented for a family vacation. The van rental is $60.00 per day, plus a $145.00 insurance fee. How many days can the van be rented if they want to spend no more than $625.00 on the van rental? Write and solve an inequality.
27
A baseball player has hit 9 home runs in 54 games. At that rate, how many home runs will he hit during a 162-game season?
3n + 1
A basket holds n apples. You pick (2n − 3) apples, and your friend picks (n + 4) apples. How many apples do you and your friend pick together? How many baskets do you need to carry all the apples?
4
A basket holds n apples. You pick (2n − 3) apples, and your friend picks (n + 4) apples. How many baskets do you need to carry all the apples?
13
A bird's nest is 12 feet above the ground. A mole's den is 12 inches below the ground. What is the difference, in feet, between the height of these two positions?
30
A boat travels 450 miles in 15 hours. What is the boat's speed in miles per hour?
160
A car can travel 480 miles on 15 gallons of gasoline. How far can it travel on 5 gallons?
300
A car can travel 80 miles on 4 gallons of gasoline. If the gas tank, which can hold about 15 gallons. How many miles can the car travel before it runs out gas?
119.66
A chain link fence is 19.3 meters long. Mr. Potter wants to make the fence 6.2 times longer. What will be the length of the new fence?
−$1.16 million
A company makes a profit of $1.38 million. This is $2.54 million more than last year. A company makes a profit of $1.38 million. This is $2.54 million more than last year. What was the profit last year?
p + 2.54 = 1.38
A company makes a profit of $1.38 million. This is $2.54 million more than last year. Write an equation to represent the profit "p" from last year.
9.475
A container has 113.7 ounces of juice. The juice is divided into 12 equal servings. How much juice is in each serving?
-2.5x < -20, x > 8
A cryotherapy chamber uses extreme cold to reduce muscle soreness. A chamber is currently 0°F. The temperature in the chamber is dropping 2.5°F every second. Write and solve an inequality that represents the numbers of seconds "x" that can pass for the temperature to drop below −20°F.
no
Are the two expressions equivalent? 3 − 5x AND 4.25 − 5x − 4.25
L = A/W
Area of a rectangle A = LW Solve for L
h = 2A/b
Area of a triangle. A= (1/2)bh Solve for h
-3 + 2
Create an expression to represent the number line.
5 + (-3)
Create an expression to represent the number line.
equivalent expressions
Expressions that have the same value but that are written in different forms.
38
Harry ran 34.2 miles while training for a track meet. He ran 0.9 miles each day. How many days did he train for the track meet?
y ÷ x
How do you calculate the constant of proportionality?
7
How many days are in a week?
365
How many days are in a year?
5,280
How many feet are in a mile?
3
How many feet are in a yard?
12
How many months are in a year?
All of them
How many months have 28 days?
One
How many solutions does an algebraic equation have?
None
How many solutions does an algebraic expression have?
Infinitely many
How many solutions does an algebraic inequality have?
Infinitely Many Solutions
How many solutions? 10 + x = x + 10
Infinitely Many Solutions
How many solutions? 2(3x + 3) = 3(2x + 2)
Infinitely Many Solutions
How many solutions? 3x + 1 = 1 + 3x
No Solution
How many solutions? 3x + 7x + 7 = 2(5x + 1)
No Solution
How many solutions? 3x - 2(3x + 5) = -5 - 3x + 15
No Solution
How many solutions? 4(2x + 1) = 5x + 3x + 9
One Solution
How many solutions? 4(x + 1) = x - 2
Infinitely Many Solutions
How many solutions? 4(x + 3) = 4x + 12
No Solution
How many solutions? 4x + 1 = 2(2x + 3)
One Solution
How many solutions? 4x + 2x - 5 = 7x - 1
Infinitely Many Solutions
How many solutions? 6(x + 1) + 5 = 13 - 2 + 6x
One Solution
How many solutions? 8(x + 2) = 2x + 16
No Solution
How many solutions? x + 5x + 4 = 3(2x - 1)
Infinitely Many Solutions
How many solutions? 2x + 8 = 2(x + 4)
Infinitely Many Solutions
How many solutions? 2x - x + 7 = x + 3 + 4
One Solution
How many solutions? 3(x - 1) = 2x + 9
One Solution
How many solutions? 4x + 2x + 2 = 3x - 7
No Solution
How many solutions? x + 2x + 7 = 3x - 7
No Solution
How many solutions? x + 2x + 7 = 3x - 9
52
How many weeks are in a year?
500-3x=26
How old am I if 500 reduced by 3 times my age is 206?
C.
If x = -1, then which of the following equations makes a true statement? A. -4x + 9 > 20 B. -4x - 5 < -15 C. -3x + 15 ≤ 18 D. -5x - 15 ≤ -22
m + 1
In a basketball game, the home team scores (2m + 39) points and the away team scores (3m + 40) points, where "m" is the number of minutes since halftime. What is the difference in the scores "m" minutes after halftime?
the independent variables
In a table or a graph, what do the "x" values represent?
the dependent variables
In a table or a graph, what do the "y" values represent?
Kind
In a word where you can be anything, be...
KIND
In a world where you can be anything, be....
straight (linear)
In order for a graph to represent a proportional relationship, the line of the graph must be _________.
origin (0,0)
In order for a graph to represent a proportional relationship, the line of the graph must pass through the _________.
33
The money used in Jordan is called the Dinar. The exchange rate is $3 to 2 Dinars. Find how many dollars you would receive if you exchanged 22 Dinars.
terms
The parts of an algebraic expression.
21
Nine items can be produced in 15 minutes. How many items can be produced in 35 minutes?
0.18x + 36 = 60
Pete rents a car for one day. The charge is $36 plus $0.18 per mile. His total charge for the car was $60.
372
Portia travels 248 miles in 4 hours. At this rate, how far can she travel in 6 hours?
x ≤ 55
The maximum speed limit is 55 miles per hour.
x/5 = -3.2
The mean temperature change is −3.2°F per day for 5 days. Write an equation to represent the total change over the 5-day period.
x ≥ 24
The minimum amount of ornaments on the tree is 24.
−7s + 7t
Simplify the expression: 2s − 9s + 8t − t
−5w + 2g
Simplify the expression: 2w − g − 7w + 3g
3q + 21
Simplify the expression: 3(2 + q) + 15
15 + 3n
Simplify the expression: 3(5 − 2n) + 9n
2m + 15
Simplify the expression: 3.5m − 1.5(m − 10)
1.4x − 5
Simplify the expression: 3.7x − 5 − 2.3x
-4h
Simplify the expression: 4h − 8h
−12s − 15
Simplify the expression: 6(3s − 2.5 − 5s)
3.5r − 7
Simplify the expression: 6.4r − 7 − 2.9r
9y + 2
Simplify the expression: 6y + 9 + 3y − 7
13p
Simplify the expression: 7p + 6p
x − 12
Simplify the expression: 7x − 2(3x + 6)
10x − 5
Simplify the expression: 8x − 5 + 2x
−x − 9
Simplify the expression: −1(x + 9)
1.5n − 3.2
Simplify the expression: −1.5(4 − n) + 2.8
−2z − 4
Simplify the expression: −1.5(8m − n)
5y
Simplify the expression: −10y + 15y
−8 + 6n
Simplify the expression: −2(4 − 3n)
−18.5s + 28.1
Simplify the expression: −2.5(2s − 5) − 3(4.5s − 5.2)
-20 + 2.5b
Simplify the expression: −2.5(8 − b)
−12x + 30
Simplify the expression: −3(4x − 10)
28 + 21d
Simplify the expression: −7(1 − 3d − 5)
16
Six tons of ore can be processed in 3 hours. At that rate, how many tons of ore can be processed in 8 hours?
p-2L/2=w
Solve P = 2L + 2w for w
d/r=t
Solve d = rt for r
r = C/2π
Solve for r C = 2πr
x = 1/2
Solve the equation. 6x + 1/4 = 13/4
x = 8.4
Solve the equation. x/2 + 1.4 = 5.6
x = 19
Solve the equation. x/5 - 2.2 = 1.6
like terms
Terms that have the same variables raised to the same exponents (terms that look alike).
reciprocal
The "flip" of a fraction
8x - 84.55 ≥ 300
The WMS basketball team is fundraising by washing cars. The team paid $84.55 for supplies. If they charge $8 per wash, how many cars must be washed to earn a profit of at least $300? Write an inequality.
x > 4
The base of the rectangle is greater than the height. Write and solve an inequality to represent the situation.
10 - 9x ≤ -73
The difference between 10 and the product of a number and 9 is -73 at maximum.
x < 20
The temperature is below 20 degrees.
x < 5
What is the inequality for the graph?
x > 2
What is the inequality for the graph?
x > 5
What is the inequality for the graph?
x ≤ 5
What is the inequality for the graph?
x ≥ -3
What is the inequality for the graph?
x ≥ 2
What is the inequality for the graph?
Subtraction
What is the inverse operation of addition?
Multiplication
What is the inverse operation of division?
Division
What is the inverse operation of multiplication?
Addition
What is the inverse operation of subtraction?
30
What is the length of the missing side?
4.8
What is the length of the missing side?
5
What is the length of the missing side?
8
What is the length of the missing side?
Isolate one positive variable on one side of the equal sign
What is the main goal of solving equations?
March
What is the month after February?
Simon
What is the name of Ms. Bixby's cat?
The Chum Bucket
What is the name of Plankton's restaurant?
The Krusty Krab
What is the name of the restaurant that Spongebob and Squidward work at?
45
What is the opposite of -45?
50
What is the opposite of -50?
64
What is the opposite of -64?
-1
What is the opposite of 1?
-81
What is the opposite of 81?
-3
What is the opposite of the opposite of -3?
$0.24
What is the unit price of a pack of 12 water bottles that cost $2.88?
$10 for 1 hour
What is the unit rate if it costs $20 for 2 hours?
$5 for 1 hour
What is the unit rate of if it costs $45 for 9 hours?
11.9
What is the unknown side length?
3.8
What is the unknown side length?
4
What is the unknown side length?
23
What is the value of I 23 I ?
1
What is the value of the expression when q = -2, r = -12 and s = 8
-24
What is the value of the expression? 38 − (− 14)
4
What is the value of the expression? −0.28 ÷ (−0.07)
20
What is the value of | -20 | ?
December
What month comes after November and before January?
WMS
What school do you attend?
Responsibility
What team are you on?
Ms. Harrington and Mrs. Malloy
When Ms. Bixby taught sixth grade, who was she on a team with?
When the inequality symbols used include ≤ or ≥.
When do we use a CLOSED CIRCLE to graph a solution set?
When the inequality symbols used include < or >.
When do we use an OPEN CIRCLE to graph a solution set?
April 1st
When is Ms. Bixby's birthday?
Tomorrow
When is your math test?
-5
Which integer describes spending 5 dollars?
Lesley University
Which school did Ms. Bixby attend for her MASTERS degree?
x > 19.3
Write and solve an inequality to find possible values of "x" so that the rectangle has a perimeter of more than 130 square units.
x > 8
Write and solve an inequality to find possible values of "x" so that the rectangle has an area of more than 130 square units.
x ≥ 37
Write and solve this inequality: Two more than twice a number is greater than or equal to seventy six.
x + 10 = 3
Write the word sentence as an equation 10 more than a number x is 3.
x - 4 = -15
Write the word sentence as an equation 4 less than a number x is −15
x - 6 = -14
Write the word sentence as an equation The difference of a number x and 6 is −14
-3 + x = -8
Write the word sentence as an equation The sum of a number x and −3 is −8.
x/-9 = -16
Write the word sentence as an equation. A number divided by −9 is −16
2/5x = 3/20
Write the word sentence as an equation. A number multiplied by 2/5 is 3/20
15x = -75
Write the word sentence as an equation. The product of 15 and a number is −75
x ÷ (-1.5) = 21
Write the word sentence as an equation. The quotient of a number and −1.5 is 21
B.
Xavier needs to bike a minimum of 80 miles this week for his training. If he has already biked 14 miles this week, then how many miles should he bike on each of the 6 remaining days this week? A. x ≥ 12 B. x ≥ 11 C. x ≤ 10 D. x ≥ 10
1/2x + 5 > 11
one-half of a number plus five is greater than eleven
13 - 4x = 1 - x
x = 4
x + 2 = 14 - x
x = 6
-13 + 4x = 1 + 2x
x = 7
8x = 3x + 35
x = 7
2x = 4x - 16
x = 8
2x - 5 = x + 4
x = 9
x < -20
x/-10 > 2
x ≥ -8
x/-2 − 6 ≤ −2
x ≥ 57
x/-3 + 18 ≤ −1
x ≤ -85
x/-5 ≤ 17
4
x/10 = 6/15
11
x/12 = 22/24
22
x/20 = 33/ 30
x ≤ -6
x/3 + 17 ≤ 15
2/5
0.4
-11
-9 + -2
-6
-9 + 3
x = -1
-9 + x = -10
-5/14
-9/14 + 2/7
-9
-90 = 10t
x = 15
-9x - 4 = -139
t < -72
-t/12 > 6
x = -13
-x + 4 = 17
x = -4
-x + 9 = 13
Patrick
"Is this the Krusty Krab?" "No, this is..."
x ≤ 15
a number is at most fifteen
18/25
0.72
39/50
0.78
4/5
0.8
19/20
0.95
48/100
0.96
- 2 1/2 + (4 1/4)
1 3/4
x < -4
10 + 4x < -6
x ≥ -2
4(-3x + 2) + 5 ≤ 37
12x - 4
4(3x - 1)
16x - 20
4(4x - 5)
x ≤ -12
4(x - 6) ≤ -12
-1.8
4.5 × (- 0.4)
x = 5
4/5x = 4
x = 10
4/5x =8
6
9/12 = x/8
0.45
9/20
12
9/x = 6/8
-27
(−16) − 6 + (−5)
x = -28
(x/4) = -7
x = 24
(x/4) = 6
x = 28
(x/4) = 7
-13.4
(−0.8) + (−7.2) − 5.4
10
(−11) − (−14) + 7
-12
(−11) − 8 + 1 − (−6)
-5.1
(−14.8) − (−9.7)
x < 2
-x - 4x > -10
x ≤ -13
-x - 5 ≥ 8
x ≤ -3
-x - 8 ≥ -5
x > -36
-x < 36
x < 63
-x/7 > -9
23/100
0.23
6/25
0.24
1/4
0.25
6/20
0.3
31/100
0.31
19/50
0.38
2/4
0.5
59/100
0.59
6/10
0.6
-0.18
0.63 ÷ (-3.5)
x < 0.5
1.2(x + 3.5) < 4.8
-2.6 + 4.1
1.5
6.513
1.7 − (−0.8) + 4.013
x = 39
1/3 x - 2 = 11
x = 39
1/3x = 13
x = 6
1/3x = 2
x < -6
1/4x < -1.5
x = 36
1/4x = 9
2/17
1/5 times 10/17
x = 20
1/5x = 4
x = 35
1/5x = 7
0.125
1/8
17
1/x = 2/34
29
1/x = 2/58
x > 10
10 + 2.5x > 35
3.124
12 + (-0.076) + (-8.8)
$15
12 footballs cost $36. How much are 5?
x = -4
12(-2x - 9) = -12
x = -7
12(-x + 5) = 144
36x - 48
12(3x - 4)
x = 2
12x - 9 = 2x + 11
15
14/10 = 21/x
42
14/x = 3/9
x > 4
14x > 56
x = -3
15 = -5x
$1.20
15 pears cost $3. How much are 6?
-7/12
15/4 + (-4 1/3)
45
15/x = 4/12
x < -3
167 < 6 + 7(2 - 7x)
x = -6
17(3x + 2) = -272
34
17/x = 1/2
x = 23
18 = x - 5
x/5 - 18 ≤ -2
18 is less than the quotient of a number and -5 is at most -2.
x > -9
19 - 4x < 55
0.955
191/200
-6x + 16
2 (-3x + 8)
$126.50
2 pizzas cost $23. How much would 11 cost?
x ≤ 3
2(-3x - 5) ≥ -28
-2x - 14
2(-x - 7)
14x + 30
2(7x + 15)
x = 12
2(x + 1) = 6x - 46
x ≤ -5
2(x - 3) + 6 ≤ -10
7
2.1 ÷ 0.3
x = 18
2/3x = 12
x = 27
2/3x = 18
x = 30
2/3x = 20
x = 15
2/5x = 6
x = 13
20 = x + 7
x > -2
3(x - 4) > -18
x = -4
2x - 3 = -11
x = -9
2x - 4 = -22
x = -5
2x - 7 = -17
x < -1
3 < -5x + 2x
$3.50
3 bananas cost $1.50. How much do 7 cost?
$180
3 pairs of shorts are $30. How much are 18?
x = 2
3(5x - 2) + 2 = 26
3x + 21
3(x + 7)
44
33/x = 6/8
x = -5
3x + 12 = -3
x = 1
3x + 12 = 15
x ≤ 2
3x + 15 ≤ 21
x = -8
3x + 2 = -22
x = 5
3x + 2 = 17
x = 4
3x + 3 = 15
x = 6
3x + 8 = 26
x = -14
3x - 6 = -48
x = 1
3x - 7 = 5x - 9
x = -2
3x = 2(7 + 5x)
x ≥ -4
3x ≥ -12
-12x + 32
4 (-3x + 8)
3.992
4 + (-0.008)
x = -6
4 = -2x + 16
x ≥ 9
4 ≤ y + (-5)
x ≤ 1
4 ≥ x + 3
x = 0
7x + 2 = 2
x = 4
7x + 8 = 36
x = 5
7x - 2 = 33
x = 0
7x+ 2 = 2
-80
8 multiplied by -10
80
8 multiplied by 10
-24x + 40
8(-3x + 5)
72x - 8
8(9x - 1)
8x - 64
8(x - 8 )
10
8/x = 12/15
40
8/x = 3/ 15
x = 3
8x + 3 = 27
x = 2
8x + 4= 20
x = -8
8x - 3 = -67
x = -20
8x - 7 = -167
x = -19
9 + x = -10
x > 20
9 -x < -11
$1.60
9 oranges cost $3.60. How much are 4?
x = -10
9(-4x - 29) = 99
D.
A fifteen passenger van is rented for a family vacation. The van rental is $75.00 per day, plus a $160.00 insurance fee. Which inequality could be used to find x, the number of days the car be rented if they want to spend less than $760.00 on the van rental? A. 75.00 + 160.00x < 760.00 B. 75.00x + 160.00 > 760.00 C. 75.00 + 160.00x > 760.00 D. 75.00x + 160.00 < 760.00
Complex Fraction
A fraction where the numerator, denominator or both contain a fraction (a fraction within a fraction).
64.5
A gallon of milk weighs 8.6 pounds. How much would 7.5 gallons of milk weigh?
x < 2.1
A jet ski rental charges a flat rate of $75, plus an additional $60 per hour. You do not want to spend more than $200. How many hours can you rent the jet ski and still be under budget?
60x + 75 < 200
A jet ski rental charges a flat rate of $75, plus an additional $60 per hour. You do not want to spend more than $200. Write an inequality to represent the number of hours ("x") that you can rent the jet ski and still be under budget?
7
A lawyer charges $100 per month to be put on retainer for a client. The lawyer also charges an hourly rate of $75 for work done. How many hours does the lawyer have to work for a client, in one month, to charge $625?
160=28+12x
A new one-year membership at RecPlex costs $160. A registration fee of $28 is paid upfront, and the rest is paid monthly. How much do new members pay each month?
x/-2 < 8
A number "x" divided by -2 is fewer than 8
x + 17 < -24
A number "x" increased by 17 is less than -24
x ≥ -2
A number is at least -2.
x ≤ 9
A number is no more than 9.
coefficient
A number multiplied by a variable (the number that comes before the variable).
constant
A number that is on its own.
$1.25
A pack of 4 t-shirt costs $5. What is the unit price for a t-shirt?
Rate
A ratio that compares two quantities with different kinds of units(include labels).
9.908
A scientist is mixing soil for his plants. He combines 4.815 kilograms of sand, 0.173 kilogram of peat moss, and 4.92 kilograms of topsoil. What is the total weight of this mixture?
50
A shopper's discount club charges a monthly fee of $15 and sells gasoline for $2.05 per gallon. The gas station across the street sells gasoline for $2.35 per gallon and charges no fee. How many gallons of gasoline would you have to buy in one month to spend the same amount at either store?
Unit Rate
A simplified ratio where the first quantity is being compared to one unit of the second quantity.
7200 + 57d
A ski resort makes snow using a snow fan that costs $1200. The fan has an average daily operation cost of $9.50. Write a simplified expression that represents the cost to purchase and operate 6 snow fans.
x + 115 ≤ 500, x ≤ 385
A small cruise ship can hold up to 500 people. There are 115 crew members already on board the ship. Write and solve an inequality that represents the additional number of people "x" that can board the ship.
14
A snail traveled 2 feet in 100 minutes. How far will it travel in 700 minutes?
3x + 2.5 = 5.05
A student bought a juice pouch for $2.50 and 3 bags of chips. The total cost was $5.05.
variable
A symbol or letter that represents an unknown value.
6 + 2x
A table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical table leaves. The extended table is rectangular with an area of (18 + 6x) square feet. Write an expression that represents the length (in feet) of the extended table.
30 + 9.75p
A three-dimensional printing pen uses heated plastic to create three-dimensional objects. A kit comes with one 3D-printing pen and p packages of plastic. An art club purchases 6 identical kits for (180 + 58.5p) dollars. Write an expression that represents the cost of one kit.
4
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. After how many hours will the two candles be the same height?
10x + 50 = 128
A waitress makes $10 an hour plus $50 in tips. Her total earning for one day was $128.
x > 5.54
A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will they have less than 100 boxes remaining? Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.
150
An assistant cook peeled 18 potatoes in 6 minutes. At this rate, how many potatoes can he peel in 50 minutes?
One Solution
An equation has _________.
Proportion
An equation that shows that two ratios are equivalent.
8.6w
An exercise mat is 3.3 times as long as it is wide. Write an expression in simplest form that represents the perimeter of the exercise mat.
algebraic expression
An expression that contains numbers, variables, operations and one or more symbols.
12 + 1.5x ≤ 60
An online music service charges a $12.00 registration fee plus $1.50 for each song downloaded. If Mary Beth has a gift card with $60.00, then how many songs can she download?
11,500 + 180n
An organization drills 3 wells to provide access to clean drinking water. The cost (in dollars) to drill and maintain the wells for n years is represented by 34,500 + 540n. Write an expression that represents the cost to drill and maintain one well for "n" years.
yes
Are the two expressions equivalent? 1.25x + 4 + 0.75x − 3 AND 2x + 1
−8(4d − 7)
Factor −8 out of −32d + 56
3.08
At Discount Copy, 12 copies cost $0.66. Melissa needs 56 copies. How much should they cost?
x ≤ 34
At most, 34 books can fit on a shelf.
x ≤ 3000
At most, an elevator can hold 3000 lbs.
16
At one store a trophy costs $12.50. Engraving costs $0.40 per letter. At another store, the same trophy costs $14.95. Engraving costs $0.25. How many letters, e, must be engraved for the costs to be the same?
2.40
At the Copy Shoppe, 18 copies cost $1.08. At that rate, how much will 40 copies cost?
75 + 12x ≥ 250
Caroline is saving to attend a week at summer camp. She needs $250 to register. Her parents will contribute $75. She plans to raise the rest of the money needed by babysitting for $12 per hour. Write an inequality to represent the minimum number of hours ("x") she must babysit in order to attend camp.
10.61
Connor bought 3 packages of donuts at $1.03 each and 2 gallons of orange juice at $3.42 each. If the tax on the items was $0.68, what was the total amount she spent?
12.5
Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
-3 + (-2)
Create an expression to represent the number line.
True
Determine whether the given value makes a true or false statement. 6m - 12 < 40, if m = 8
False
Determine whether the given value makes a true or false statement. c - 12 > 30, if c = 13
True
Determine whether the given value makes a true or false statement. k + 8 ≥ 19, if k = 11
False
Determine whether the given value makes a true or false statement. k+ 6 ≥ 19, if k = 11
A.
Emily is encouraged to read more than 4 hours each week. It takes her 45 minutes to finish her first book. She divides the remainder of the time equally amongst the other six days. What is the minimum number of minutes she should read each day? A. x > 32.5 minutes B. x > 40 minutes C. x ≤ 32.5 minutes D. x ≤ 40 minutes
3
Evaluate 10 + (-10) + 3
0
Evaluate 7 + (-9) + 2
- 4/5
Evaluate the complex fraction
-1 1/5
Evaluate the complex fraction
-1 7/19
Evaluate the complex fraction
1/9
Evaluate the complex fraction
17 1/2
Evaluate the complex fraction
-1.25(x + 4)
Factor out the coefficient. -1.25x - 5
1.7( j − 2)
Factor the expression: 1.7j − 3.4
5(3x + 5)
Factor the expression: 15x + 25
8(2n − 3)
Factor the expression: 16n − 24
6(3a − 2)
Factor the expression: 18a − 12
−5(p − 4)
Factor the expression: −5p + 20
−12(2k − 10)
Factor −12 out of −24k + 120
−4(2k + 3)
Factor −4 out of −8k − 12
−5(d − 6)
Factor −5 out of −5d + 30
x+x+2+x+4+x+6=56
Find four consecutive odd integers whose sum is 56.
0.5b + 7
Find the difference: (4 − 3.7b) − (−5.4b − 4) − (1.2b + 1)
2y + 12
Find the difference: (4y + 3) − (2y − 9)
2m − 15
Find the difference: (m − 3) − (−m + 12)
−8.3c − 15
Find the difference: (−2c + 5) − (6.3c + 20)
1/20
Find the product of -2/11 and -11/40
−11n + 11
Find the sum: (4.5 − n) + (−10n + 6.5)
8z − 2
Find the sum: (5z + 4) + (3z − 6)
4c + 5
Find the sum: (c − 4) + (3c + 9)
3x + 2
Find the sum: (x + 3) + (2x − 1)
0.9m − 12
Find the sum: (−2.1m − 5) + (3m − 7)
−3
Find the sum: (−8z + 4) + (8z − 7)
2.5x + 3 = 5.05
Hadlee bought scrunchies for $2.50 each and paid $3 in tax for her purchase. Her total was $5.05.
Worries
Hakuna Matata. It means no ___.
3n and -n, 7 and -3
Identify the like terms in the expression: 3n + 7 − n − 3
3z and 4z, 4 and 2
Identify the like terms in the expression: 3z + 4 + 2 + 4z
4p and p, 7 and -5
Identify the like terms in the expression: 7 + 4p − 5 + p + 2q
8x and 2x
Identify the like terms in the expression: 8x − 5 + 2x
60
If 5 pencils cost 20 cents, how much would 15 pencils cost?
25.80
If 8 bags of chips costs $10.32, how much will you pay for 20 bags?
6 and 2/3 miles
If Jim runs 5 miles in 3/4 of an hour, how many miles can he run in 1 hour?
325
If John can travel 130 miles in 2 hours, how far can he travel in 5 hours if he travels at the same rate of speed?
No
Is 1.7 a solution to x ≤ -1.6?
Yes
Is 4 a solution to x ≥ -6?
175 + 35x ≤ 600
Jasmine has a budget of $600.00 to spend on home renovations. She will spend $175.00 on a new sink and the remainder on countertops. The countertops cost $35 per square foot. What is the maximum number of square feet Jasmine can purchase?
20
Jenny can send texts on her phone at the rate of 32 words per minute. If she sends 8 texts that average 80 words each, about how long would it take her?
x < 11.2
JoAnn has a bank account with $350.00 in it. Every week, she withdraws $12.50 to attend the movies. What is the maximum number of weeks that JoAnn can withdraw the money without allowing her bank account to drop below $210.00?
300 - 12.5x > 250
JoAnn has a bank account with $350.00 in it. Every week, she withdraws $12.50 to attend the movies. Write an inequality to represent the maximum number of weeks ("x") that JoAnn can withdraw the money without allowing her bank account to drop below $210.00.
$0.99
John bought 8 Kit-Kats for $7.92. What is the unit price for the Kit-Kats?
45
Jonathan purchased 120 pieces of candy for Valentine's Day. He gives 2 pieces to each of his friends. When he finishes handing out candy, he has 30 pieces left. How many friends did he give candy to?
35+0.50x=52
Juan's cell phone company charges $35 a month for phone service plus $0.50 for each text message. How many text messages does Juan send in a month if his bill was $52?
x ≤ 56.6
Marco is limited to 7 hours of screen time each week. He decides to watch a movie that is 1 hour and 20 minutes on Sunday. If he divides the remainder of the time equally amongst the other six days, then how many minutes can he watch each day? Write and solve an inequality.
3
Mark walked three-quarters of a mile in fifteen minutes. How many miles can he walk in an hour?
6m + 2
Mars has "m" moons. The number of moons of Pluto is one more than twice the number of moons of Mars. The number of moons of Neptune is one less than 3 times the number of moons of Pluto. Write a simplified expression that represents the number of moons of Neptune.
115
Mary ran 2 miles in about 23 minutes. If she continues at the same pace, how long will it take her to run 10 miles?
A.
Match the inequality statement to the appropriate graph. x < 6.5
E.
Match the inequality statement to the appropriate graph. x > 6.5
D.
Match the inequality statement to the appropriate graph. − 1/2 < x
C.
Match the inequality statement to the appropriate graph. − 1/2 ≥ x
x ≥ 11.25
Megan is saving up to buy a new cell phone that costs $220.00. So far she has saved $175.00. Megan would like to buy the cell phone in four weeks. Write and solve an inequality to represent at least how much she must save every week to purchase the cell phone.
2
Michael and Kevin are running. Kevin gets a 3-mile head start and runs at a rate of 5.5 mi/h. Michael runs at a rate of 7 mi/h. How many hours will it take Michael to catch up with Kevin?
121-4x=9
Ming won 121 lollipops playing basketball at her school's game night. Later, she gave four to each of her friends. She only has 9 remaining. How many friends does she have?
x ≥ 15
Missy is saving to attend a week at summer camp. She needs $250.00 to register. Her parents will contribute $75.00. She needs to raise the rest of the money babysitting for $12.00 per hour. What is the minimum number of hours she must babysit in order to attend camp?
the Romans
Mr. Casey teaches Math on which 6th grade team?
the Aztecs
Mr. Howell teaches AC on which 6th grade team?
the Romans
Mr. Zerdelian teaches Science on which 6th grade team?
0.28
Mrs. Smith paid $5.32 to buy a pen for each student in his class. Her class has 19 students. How much did each pen cost?
the Aztecs
Ms. Harrington teaches L+L on which 6th grade team?
3
Netflix charges David $15 per month for a membership, plus a $5 one-time fee for streaming on his phone. How many months will David have his membership for if Netflix charges him $50?
The Patriots
New England's football team.
2,100
Of the 50 fish that Jim caught from the lake, 14 were trout. The estimated population of the lake is 7,500 fish. About how many trout would you expect to be in the lake?
9
On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games, g, were bowled?
15
One scooter and two identical bikes are for sale. Each bike is $7 more than the scooter. If the total value of the items is $59, then find the value of the scooter.
D.
Paulo's grandfather gave him a collection of 20 coins. Each month Paulo adds 4 coins to his collection. Which inequality can be used to find m, the number of months after starting his collection when Paulo will have more than 50 coins in his collection? A. 20m + 4 < 50 B. 20 + 4m < 50 C. 20m + 4 > 50 D. 20 + 4m >50
280
Pep Club members are making spirit buttons. They make 490 spirit buttons in 3.5 hours. How many buttons can they make in 2 hours?
L = (P - 2W)/2
Perimeter of a rectangle. P= 2L + 2W Solve for L
S = P/4
Perimeter of a square. P=4S Solve for S
9
Rosemary had $37 to spend on school supplies. She buys some packages of mechanical pencils for $4 each. After her trip to the store, she only has $1 left. How many packs of pencils did she buy?
200
Ruby weighs 88 lbs. Her weight is 12 lbs. less than half her father's weight. How much does her father weigh?
28.5 + 3x ≤ 80
Russell wants to buy three ties and a belt and must spend no more than $80.00. The belt costs $28.50. If the three ties are the same price, then how much can he pay for each tie?
25
Ryan goes to the mall with his friends after school. At the mall, he purchases 4 pairs of basketball shorts and a pair of sneakers for $100. If he spends a total of $200, how much money did he spend on each pair of basketball shorts?
x ≤ 64
Ryan is planning a party for his parents' anniversary. The caterer charges a deliver fee of $14 plus an additional $5.25 per person. If Ryan can spend no more than $350, how many people can he invite?
4 11/14
Ryder rode 3 and 1/7 miles on his bicycle yesterday. He rode 1 and 9/14 miles today. How many miles did he ride during these two days?
x > 54
SOLVE AN INEQUALITY Dennis is selling chocolate bars for a fundraiser, and if he sells over $175 worth of candy, he'll win a prize. If chocolates sell for $2.50 a bar, and Dennis has already sold $40 worth of candy, then how many more bars does he have to sell in order to win a prize?
x ≤ 5
SOLVE AN INEQUALITY Jamal has $15.00 to spend at the concession stand. He buys nachos for $7.50, and he wants to purchase some Sour Straws for $1.50 each. How many Sour Straws can Jamal purchase with the money that he has?
x > 37.5
SOLVE AN INEQUALITY Liza wants to have more than $750 in her savings account before she will leave for college. Right now she has $300, and she is going to babysit to earn $12.00 an hour. How many hours will Liza need to babysit before she leaves for college?
x ≥ 11
SOLVE AN INEQUALITY Marcus needs to bike at least 80 miles this week for his training. If he has already biked 25 miles this week, then how many miles should he bike on each of the 5 remaining days this week?
x ≤ 7
SOLVE AN INEQUALITY Taylor has a $30.00 gift card that she can spend at the store. She has already bought a $9.00 picture frame, and she wants to buy $3.00 journals with the leftover money on the card. How many journals can she buy without going over the card's limit?
x ≥ 12
SOLVE AN INEQUALITY The amusement park won't allow kids to ride roller-coasters until they are a minimum of 48 inches tall. Michael is now 42 inches tall, and grows about 1/2 inch every month. How many months will it be until Michael can ride a roller-coaster?
4+3x=19
Sandra scores 4 baskets in his first basketball game. She then scored the same number of baskets in each of her next 3 games. If Sandra made 19 baskets total, how many baskets did she score in each of the three games?
7x + 1.5 = 11.50
Seven friends go to the movies. They each get a ticket and share one bucket of popcorn for $1.50. Their total cost is $11.50.
3/5x + 7 ≥ 31
Seven more than three-fourths of a number is no less than 31.
350
Seven out of every twelve people have brown eyes. If 490 people have brown eyes, how many do not?
8r − 17
Simplify the expression: (2r − 13) − (−6r + 4)
11j + 4
Simplify the expression: (3j + 11) + (8j − 7)
−2z + 22
Simplify the expression: 14 − 3z + 8 + z
2a − 6
Simplify the expression: 2(a − 3)
−6s − 8
Simplify the expression: 2(−3s + 1 − 5)
8h − 12.75
Simplify the expression: 2.25 − 2(7.5 − 4h)
−9.8g
Simplify the expression: 2.4g − 2.4g − 9.8g
6.5w − 3y
Simplify the expression: 2.5w − 3y + 4w
6.8x − 5
Simplify the expression: 2.5x + 4.3x − 5
−6m
Simplify the expression: 2m - m - 7m
400
The ratio of athletes to non-athletes at Taylor middle school is 3 to 4. If there are 300 athletes, how many non-athletes are there?
24
The ratio of seventh graders to eighth graders participating in the science fair is 4:3. There are 18 eighth graders participating in the science fair. How many 7th graders are there?
4
The ratio of teachers to students needs to be 1:30. If there were 120 students, how many teachers would be needed?
2x + 20
The rectangular pupil of an octopus is estimated to be 20 millimeters long with an area of (20x − 200) square millimeters. Write an expression that represents the perimeter (in millimeters) of the octopus pupil.
x > 99
The student weighs more than 99 lbs.
28
The sum of 16 and 12
11.71
The sum of 2.31 and 9.4
0
The sum of an integer and it's additive inverse always equals _________.
0
The sum of an integer and it's opposite always equals _________.
108.9
The sum of the measures of the angles of a triangle equals 180°. What is the missing angle measure?
x+x+2+x+4=39
The sum of three consecutive odd numbers is 39. What is the smallest of these numbers?
2x + 15 > 3
The sum of twice a number and 15 is greater than 3.
4.8
The total weight of 32 math books is 153.6 pounds. If each book is the same weight, what is the weight of 1 math book?
x ≥ 48
The youth soccer team is fundraising by washing cars. They paid $84.55 for supplies. If they charge $8.00 per wash, how many cars must be washed to profit at least $300.00 dollars?
6x + 24 = 276
There are 276 seventh graders going on a field trip. The school ordered seven buses to transport students. The last bus has 24 students on it, and the rest of the buses all have the same number of students. Write an equation that represents this situation. Let "x" represent the number of students on the buses other than the last bus.
18
To make lemonade, you need 6 lemons and 8 cups of water. How many lemons do you need if you have 24 cups of water?
add the opposite of the second/third/fourth... rational number.
To subtract rational numbers you must...
x ≤ 6
Translate and Solve: Five times a number decreased by eight is at most ten more than twice the number.
x > 6
Translate and Solve: Negative three times a number increased by seven is less than negative eleven.
x ≥ 7
Translate and Solve: The sum of a number and fourteen is less than or equal to three times the number.
x > 7
Translate and solve: A number decreased by 12 is greater than -5.
x < 8
Translate and solve: A number increased by 1 is less than 9.
x ≤ -1
Translate and solve: A number plus 2 is at most 1.
x ≤ -25
Translate and solve: Seven more than a number is less than or equal to -18.
x ≥ 35
Translate and solve: Twenty less than a number is at least 15.
2x ≤ 3.5
Twice a number "x" is at most 3.5
x < 36
Twice a number "x" is fewer than 72
340
Two friends rent an apartment together. They agree that Joe will pay 1.5 times what Mike pays. If the rent is $850, how much will Mike pay?
20
UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many additional pounds, p, will it take for UPS and FedEx to cost the same?
7.5 + 1.5x ≤ 15
WRITE AN INEQUALITY Jamal has $15.00 to spend at the concession stand. He buys nachos for $7.50, and he wants to purchase some Sour Straws for $1.50 each. How many Sour Straws can Jamal purchase with the money that he has?
12x + 300 > 750
WRITE AN INEQUALITY Liza wants to have more than $750 in her savings account before she will leave for college. Right now she has $300, and she is going to babysit to earn $12.00 an hour. How many hours will Liza need to babysit before she leaves for college?
5x + 25 ≥ 80
WRITE AN INEQUALITY Marcus needs to bike at least 80 miles this week for his training. If he has already biked 25 miles this week, then how many miles should he bike on each of the 5 remaining days this week?
9 + 3x ≤ 30
WRITE AN INEQUALITY Taylor has a $30.00 gift card that she can spend at the store. She has already bought a $9.00 picture frame, and she wants to buy $3.00 journals with the leftover money on the card. How many journals can she buy without going over the card's limit?
0.5x + 42 ≥ 48
WRITE AN INEQUALITY The amusement park won't allow kids to ride roller-coasters until they are a minimum of 48 inches tall. Michael is now 42 inches tall, and grows about 1/2 inch every month. How many months will it be until Michael can ride a roller-coaster?
Today
What do we call the day after yesterday but the day before tomorrow?
Common denominators
What do you need to add or subtract fractions?
y = kx
What equation can be used to represent the relationship in a table or graph that displays proportional relationships?
-9/50
What is -0.18 as a fraction in simplest form?
-5.888...
What is -5 8/9 as a decimal?
-5 24/50
What is -5.96 as a fraction in simplest form?
Wildcats
What is WMS's mascot?
Wildcat
What is Wilson's mascot?
Subtraction
What is the Inverse Operation of Addition?
Multiplication
What is the Inverse Operation of Division?
Division
What is the Inverse Operation of Multiplication?
Addition
What is the Inverse Operation of Subtraction?
14
What is the absolute value of -14?
7
What is the absolute value of -7?
13
What is the absolute value of 13?
9
What is the absolute value of 9?
$2.50
You and 4 friends are buying tickets for a concert. The cost to buy one ticket is "c" dollars. If you buy all the tickets together, there is a discount and the cost is (5c − 12.5) dollars. How much do you save per ticket when you buy the tickets together?
7h + 9
You and a friend collect seashells on a beach. After "h" minutes, you have collected (11 + 2h) seashells and your friend has collected (5h − 2) seashells. How many total seashells have you and your friend collected?
4x+20=100
You and three friends go to the town carnival. You have a coupon for $20 off that will save your group money! If the total bill to get into the carnival was $100, how much does one regular price ticket cost?
x ≤ 16
You are organizing books on a shelf in your room. Each book has a width of 1 ½ inch. Write and solve an inequality for the maximum number of books "x" that can fit on a shelf that measures 24 inches.
2/3x ≤ 18
You are organizing books to fit on a shelf in your room. The shelf is 18 inches long. Write an inequality that represents the maximum number of books ("x") that can fit on your shelf if each book has a width of ⅔ inch.
3/4x ≤ 24, x ≤ 32
You are organizing books to fit on a shelf in your room. The shelf is 24 inches long. Write and solve inequality that represents the maximum number of books "x" that can fit on your shelf if each book has a width of ¾ inch.
2x+3=19
You bought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
4m + 8
You burn 265 calories running and then 7 calories per minute swimming. Your friend burns 273 calories running and then 11 calories per minute swimming. You each swim for the same number of minutes. Find the difference in the amounts of calories burned by you and your friend.
6
You can buy 2 hot dogs for $3. How much would it be for 4 hot dogs?
75
You estimate that you can do 12 math problems in 45 min. How long should it take you to do 20 math problems?
6w + 8
You expand a rectangular garden so the perimeter is now twice the perimeter of the old garden. The expression 12w + 16 represents the perimeter of the new garden, where w represents the width of the old garden. Write an expression that represents the perimeter of the old garden.
4x+11=23
You had $23 to spend on four avocados. After buying them you had $11. How much did each avocado cost?
x ≥ 7
You have $100 to buy Funko Pops. Each Funko Pop costs $12. What is the maximum number of Funko Pops that you can buy and still have at least $10 left?
x ≤ 24
You have $130 to buy baseball cards. Each pack of cards costs $5. What is the maximum number of packs of baseball cards can you buy and still have at least $10 left?
4x + 28 ≥ 100
You have to spend at least $100 on your online order to be eligible for free shipping. You have already spent $28 on a sweatshirt and plan to buy several pairs of socks ("x") that cost $4 each. Write an inequality that could be used to represent the situation.
$228
You want to buy a bicycle with your friend. You have $43.50 saved and plan to save an additional $7.25 every week. Your friend has $24.50 saved and plans to save an additional $8.75 every week. After 10 weeks, you and your friend use all of the money and buy the bike. How much does the bike cost?
16w + 68
You want to buy a bicycle with your friend. You have $43.50 saved and plan to save an additional $7.25 every week. Your friend has $24.50 saved and plans to save an additional $8.75 every week. Simplify an expression that represents the amount of money you and your friend save after "w" weeks.
-30
c/6 = -5
x - 4 ≥ 6
four less than a number is at least negative six
x > #
is greater than, is more than, is larger than, above...
x < #
is smaller than, is less than, below...
-16
k/4 = -4
14
m - 5 = 9
-28
m/-2 = 14
x ≤ #
maximum, at most, not more than, is not greater than...
x ≥ #
minimum, at least, is not less than, not smaller than...
-6 + x ≤ 15
negative six plus a number is less than or equal to fifteen
x - 13 ≥ 1
the difference between a number and thirteen is at least one
x ÷ -2 ≥ 10
the quotient of a number and negative two is greater than or equal to ten
improper fraction
when multiplying fractions I must change a mixed number to a/an
x ≤ 1
x + (-4) ≤ -3
x > 5
x + 11 > 16
x ≤ -5
x + 2 ≤ -3
x = 3
x + 3 = 3(11 - 3x)
x ≥ -2
x + 3 ≥ 1
x ≤ -90
x + 45 ≤ -45
x ≥ 11
x + 7 ≥ 18
x < -1
x + 9 < 8
x = 4
x + 9 = 13
x < -6
x - 1 < -7
x = 2
x - 3 = -1
x > -6
x - 3 > -9
x ≤ 6
x - 5 ≤ 1
x = 32
x - 7 = 25
x > -6
x - 7 > -13
-6x + 20 = -2x + 28
x = -2
6x - 8 = 9x + 1
x = -3
-3x - 15 = -6x - 27
x = -4
-5x + 2 = 4x + 47
x = -5
6x + 7= 13 + 7x
x = -6
2x + 7 = 4x + 23
x = -8
75 + 14x = 4x - 15
x = -9
5 + 3x = 2x + 6
x = 1