Math, Chapter 9: Expressions and Equations.

Which is a simplified form of the expression -4(n + 1) - (n + 2)?

-5n - 6

Solve: p + 6 = 23

17

A formula for finding SA, the surface area of a rectangular prism, is SA = 2(ab + ac + bc), where a, b, and c represent the lengths of the edges of the prism. What is the surface area of this prism if a = 12 inches, b = 6 Inches, and c = 4 inches?

288 in. 2

Simplify: -(n + 2) + 3(n - 2)

2n - 8

Solve the equation -6 + 6n = 42 for n.

8

Nerissa paid a total of $8 for 4 packs of pencils she purchased from the convenience store. Let p represent the cost of one pack of pencils. Which equation shows an equality between two different ways of expressing the cost for all the pencils?

8 = 4p

Activity Quiz:

Algebraic Expressions

How can we represent 9 less than the number m?

m - 9

Which of the following values of n will result in a true statement when substituted into the given equation? 4n + 9 = 1

n = -2

Solve for x: 7x = 63

x = 9

If a and b are real numbers, which equation represents the Associative Property of Multiplication?

(a • b) • c = a • (b • c)

Which is a simplified form of the expression -9(g + 2) - (g + 2)?

-10g - 20

Which is a simplified form of the expression -5(y - 2) - 7y?

-12y + 10

Evaluate when x = 3, y =-3 and z =-2: xy + 2z

-13

Simplify: -10(x - 7) - 3x

-13x + 70

Which is a simplified form of the expression -4(3r - 2) - 2(r + 1)?

-14r + 6

Simplify: 4z - 7(3z - 4)

-17z + 28

Simplify: -12f - 3(2f + 2)

-18f - 6

Which is a simplified form of the expression -2b - 3(2b+1)?

-8b - 3

Solve the equation 4y - 3 = 1 for y.

1

Which of the following numbers is the product of the number p and its multiplicative inverse 1/p?

1

Solve the equation 14 + 14p = 21 for p.

1/2

Solve the equation 28 + 24p = 36 for p.

1/3

A large pizza is cut into 12 slices, so several friends can each have 3 slices. If p represents the number of friends, which equation shows an equality between two different ways of expressing the number of slices?

12 = 3p

The value of the nth term in a sequence of numbers is given by the expression 2n - 3. What is the 8th term in the sequence?

13

Solve the equation -25 + 4y = 35 for y.

15

Solve the equation 2q - 4 = 26 for q.

15

Which is a simplified form of the expression 6(2t - 3) + 3(t + 5)?

15t - 3

Simplify: (16-5) - 9 x 1

2

Solve the equation -8v -5 = -21 for v.

2

Solve the equation -9v - 9 = -27 for v.

2

Solve the equation 9r - 2 = 16 for r.

2

The value of the nth term in a sequence of numbers is given by the expression 5n + 2. What is the 4th term in the sequence?

22

Alexa is y years old. Nate is 22 years old, and Alexa is one-half Nate's age. Which equation shows an equality between two different ways of expressing Nate's age?

22 = 2y

Katie has f fish. Alejandro has 11 fish, which is 3 fewer than twice the number Katie has. Which equation shows an equality between two different ways of expressing how many fish Alejandro has?

2f - 3 = 11

Solve the equation 18 = 3 + 5x for x.

3

Solve the equation 52y - 29 = 10 for y.

3/4

Simplify: 6s - (3s - 2)

3s + 2

Which is a simplified form of the expression 4(2z - 1) - 5z?

3z - 4

Solve the equation -15 + 10y = 25 for y.

4

Solve the equation -4 + 4a = 12 for a.

4

Solve the equation 12 + 2n = 20 for n.

4

Evaluate when x = 3, y = 2, and z = 4: z/x + y

4/5

Reggie wrote a total of 48 political articles for the town newspaper this year. The number of political articles he wrote is 3 less than twice the number of sports articles he wrote. Let s represent the number of sports articles he wrote. Which equation shows an equality between two different ways of expressing the number of political articles that Reggie wrote this year?

48 = 2s - 3

A formula for finding A, the area of a triangle is A= 1/2 bh, where b is the base of the triangle and h is the altitude to that base. In this triangle, If b=16 inches, and h = 6 inches, what is the area of this triangle?

48 in. 2

Teemu weighs 4 times as much as his bike. Teemu weighs 192 lb. Let w represent the weight of Teemu's bike in pounds. Which equation shows an equality between two different ways of expressing Teemu's weight in pounds?

4w = 192

Brianna is 2 years less than 4 times the age of Zack. If Zack's age in years is y, which expression represents Brianna's age?

4y - 2

Francesca is making a recipe that calls for 5 cups of flour. In total, she has 25 cups of flour. Let f represent the amount of flour she has left after making the recipe. Which equation shows an equality between two different ways of expressing the amount of flour Francesca uses in the recipe?

5 = 25f

The formula for finding the sum of the whole numbers from 1 to any whole number, n, is n(n+1)/2. Using this formula, find the sum of the whole numbers from 1 to 10.

55

Simplify: 2(d + 3) + 3(d - 3)

5d - 3

Which is a simplified form of the expression 3(m + 1) + 2m?

5m + 3

Simplify: 4y + (2y - 4)

6y - 4

Solve the equation -3h + 6 = -15 for h.

7

Activity Quiz:

Expressions

Activity Quiz 1:

Expressions and Equations

Write the equation 12 = -3x + 6 in the form ax + b = c, with c = 12. What are the values of a and b?

a = -3, b = 6

Solve: a - 17 = 15

a = 32

Which of the following illustrates the Distributive Property of Multiplication over addition?

c(-3) + c(d) = c(-3 + d)

Brooke wants to build a tree house. She wants the tree house to be 3 ft. more than half the height of the tree. If the tree is h feet tall, how can Brooke represent how high she wants the tree house to be?

h/2 + 3

Which is a simplified form of the expression 2(2j + 3) - 3j?

j + 6

Which of the following values of m will result in a true statement when substituted into the given equation? m - 1.9 = 2.2

m = 4.1

Solve for n: n - 17 = 3

n = 20

Solve for n: n/20 = 1

n = 20

Solve: 5n = 25

n = 5

Which is a simplified form of the expression -3p - 4 + 4p + 8?

p + 4

Solve for p: 25 = 5p/4

p = 20

Solve: 12 = p/2

p = 24

Solve: q + 24 = 24

q = 0

Joe ran half the distance that Phil did. If the distance that Phil ran is represented by r which expression represents the distance that Joe ran?

r/2

Which of the following values of t will result in a true statement when substituted into the given equation? 1/2t - 4 (2 + t) = 20

t = -8

Solve: 14y = 7

y = 1/2

Solve for y: 9y = 36

y = 4

Solve for you: 4y = 32

y = 8

Solve the equation 2 = -6 - 20x for x.

-2/5

Simplify: 5(y + 1) + 5(y - 1)

10y

Which expression represents 12 times a number, n, minus 6?

12n - 6

Simplify: 6(6k + 7) - 7k

29k + 42

Which is a simplified form of the expression 2(y + 1) + 2 (y - 2)?

4y - 2

Hank went to an apple orchard and paid an entrance fee of $5 and bought a pounds of apples at $2 per pound. Hank paid a total of $19. Which equation shows an equality between two different ways of expressing how much Hank paid in all?

5 + 2a = 19

Solve the equation 4m = 28 for m.

7

What is the multiplicative inverse of the fraction 2/7?

7/2

Solve the equation -21 + 25n = 14 for n.

7/5

Solve the equation -21 + 70n = 77 for n.

7/5

The cheer squad had j members. Eight new students joined the squad. Which expression represents how many people are on the squad now?

8 + j

Which expression represents eight times a number, v?

8v

For real numbers c and d, what property of real numbers is illustrated by the equation below? c + d = d + c

Commutative Property of Addition

Activity Quiz 2:

Expressions and Equations

Activity Quiz:

Properties

Activity Quiz 1:

Simplify Algebraic Expressions

Activity Quiz 2:

Simplify Algebraic Expressions

Activity Quiz 1:

Solve One-Step Linear Equations

Activity Quiz 2:

Solve One-Step Linear Equations

Activity Quiz 1:

Solve Two-Step Linear Equations

Activity Quiz 2:

Solve Two-Step Linear Equations

Activity Quiz:

Subsitution

The formula for perimeter of a square with side length s is P = 4s. If the length of each side of the square is tripled, how is the perimeter affected?

The perimeter is three times as great.

The formula for finding the perimeter of a rectangle with length, I, and width, w, is P = 21 + 2w. If the length and width of a rectangle are both doubled, how is the perimeter affected?

The perimeter is twice as great.

Solve for a: a - 17 = -15

a = 32

There were c members in the chess club before 8 more people joined. Which expression describes the number of members in the chess club now?

c + 8

Lorenzo is building a bookshelf. He wants the bookshelf to be 1.5 feet taller than 1/4 the height of his plant stand. If p equals the height of Lorenzo's plant stand, which expression represents the height of the bookshelf?

p/4 + 1.5

Solve for q: q + 12 = -12

q = -24

Which of the following values of r will result in a true statement when substituted into the given equation? 2(4r + 4) = -16

r = -3

Which of the following values of r will result in a true statement when substituted into the given equation? -r + 5(r+2) = -10

r = -5

Ana Maria has 1/3 the length of ribbon Jolie has. If r represents the length of ribbon Jolie has, which expression represents the length of Ana Maria's ribbon?

r/3

Solve for t: t + 7 = 21

t = 14

Solve for t: t + 1 = 24

t = 23

Solve for t: 18t = 72

t = 4

Francis is 9 years older than Vincent. Francis is 17 years old. Let v represent how old Vincent is. ​

v + 9 = 17

Mahimi has x dollars for food. She wants to buy lunch and still have $2 left over to buy a snack later. How can Mahimi represent how much she can spend on lunch?

x - 2

Solve for x: x + 18 = -37

x = -55

Solve for x: x - 7 = 4

x = 11

Solve for x: x/4 = 16

x = 64