Solving Equations and Inequalities
-24 < 3x + 3 < -3
-9 < x < -2
-3 -x = 1 -(x + 4)
All Real Numbers
-5(x + 3) ≤ -15 - 5x
All real numbers
8 + 10k ≥ 10 + 9k or 8 - 8k ≥ -5k - 10
All real numbers
3(x-5) -10 = 2 -(1-3x)
No solution
5/3 - x = -x -5/3
No solution
6 < 7(x + 1) - (1 + 7x)
No solution
6x + 4 ≥ 10x + 8 and -4x + 6 ≤ -3x -8
No solution
4 + 2k ≥ 22 or 2 - 6k > 44
k ≥ 9 or k < -7
m - 1 > 9 or 4 - 2m < 10
m > -3
-m + 4 ≤ m + 8
m ≥ -2
-156 > 10n + 4
n < -16
8n + 5 = 6n - 3
n = -4
10 - 3n ≥ -2 and 9n + 3 < 93
n ≤ 4
3(2 - 7n) - 5n ≤ -202
n ≥ 8
-10 + p/4 < -10
p < 0
-5v < 45
v > -9
9v - 1 > 7 + 7v or 6v - 2 > 9v + 7
v > 4 or v < -3
v - 9 ≤ -28
v ≤ -19
3x + 5 < 35 and 4 + 8x ≥ 12
x < 10 and x ≥ 1
x/2 - 1 = -7
x = -12
21 + 6x = -3
x = -4
-4x - 2 = -3 -3x
x = 1
-2 + 14x - 5 = 12 + 11x + 5 - 2x
x = 24/5
5(x - 3) = 10
x = 5
3x + 4(x - 2) -x = 7
x = 5/2
3/4x - 6 = 10
x = 64/3
3/4 - 2/3x 1/6 + 3x
x = 7/44
7 = 2(x - 1) - x
x = 9
Jimmy's homework average in English class is 92. The text average is worth 75% of the final grade, and homework is worth 25% of the final grade. What test average does Jimmy need in order to have a final grade of at least 80?
x = Jimmy's test average At least a 76% test average
A lawyer charges an initial fee of $150 and $250 per hour of advising. If Michael's lawyer charged him a total of $2400, how many hours of legal advice did he receive?
x = number of hours 9 hours
Adam is looking to sign up for a new gym. Each month, Deluxe Sports charges $60 plus $35 for each training session. Athlete's Alley charges $100 and $25 per training session. How many training sessions would make the two gyms cost the same amount?
x = number of training sessions 4 sessions
Julia is trying to decide if she should purchase a season pass to an amusement park for $235 or pay $38.50 per visit and wants to know when it will be cheaper to buy the season ticket. How many visits to the park make the season pass a better buy?
x = number of visits more than 6 visits
In a week, Jack can work 20 regular hours and 4 overtime hours and get paid the same as if he worked 16 regular hours and 6 overtime hours. If he gets paid $20 for every overtime hour, what is his regular hourly pay?
x = pay per regular hour $10 per regular hour.
A charity is planning to raffle off a new car donated by a local car dealer. The charity wants to raise at least $70,000. It expects to sell 1250 tickets and to spend $5000 promoting the raffle. What should the tickets price to reach their goal?
x = price per ticket At least $60 each
The product of -3 and 6 less than a number is double the sum of the same number and two. Find the number.
x = the unknown number The number is 14/5
Triple a number is 18 more than the same number. Find the number
x = unknown number The number is 9
-4(1 - 7x) > -200
x > 7
