Unit 3 Study Guide
NAME _________________________
BLOCK _________________________
Solve each inequality.
1. x − 5 <− 2
2. 1 >− 3 + x
3. x + 6 < 10
4. − 5q≥ − 10
5. 4x <− 16
6. − 1 <
7.
5m
6
v
−5
> 10
8. Identify the error and describe it. Share a strategy the student could use to prevent the same error
in the future. Then, solve the problem correctly.
Problem
Identify and Explain the Error
x ≤40
5
( 5x )·5≤40
5
x≤8
Correct Solution
Helpful Strategy
Write and solve an inequality for each statement.
9. Two is greater than the sum of 3 and one-fourth of a number
Inequality: _________________________________
solution: _______________
10. The product of -2 and the sum of a number and 3 is at least 0.
Inequality: _________________________________
Solve each inequality.
11. 5x + 4 < 11 − 2x
12.
2(2x − 8) − 8x≤0
13. 5x − 4 > 4 − 3x
14.
x
3
− 1≤ 2x + 3
15. − 3(− 7b − 6) − 7 < p − 29
solution: _______________
Write an inequality and solve the problem algebraically.
16. Elisa won 40 lollipops playing basketball at the school fair. She gave two to every student in her
math class. She has at least 7 lollipops left. Find the maximum number of students in her class.
17. More than 450 students went on a field trip. Ten buses were filled and 5 more students traveled
in a car. Find the minimum number of people on each bus.
18. Al earns $5.95 per hour working after school. He needs at least $215 for his holiday shopping.
How many hours must he work to reach his goal?
19. A club can buy ready-made shirts for $14.50 each. Alternately, it can buy plain T-shirts for $6.25
each, fabric paint for $35.70, and a pack of stencils for $8.50. ​Write an inequality​ to represent how many
shirts will need to be purchased to that stenciling plain T-shirts will be cheaper than buying ready-made
shirts.
Katelynn wrote the following inequality to represent the previous statement. What is her error?
Correct it, then solve.
$14.50x ≤ $6.25x + $35.70 + $8.50x
x is the number of shirts
20. Mrs. Smith wrote “Eight less than three times a number is greater than fifteen” on the board. If x
represents the number, which inequality is a correct translation of this statement?
a. 3x − 8 > 15
b. 3x − 8 < 15
c. 8 − 3x > 15
d. 8 − 3x < 15
21. ​Max's employer has at most $18.00 to spend on tape measures for his crew. How many can he
buy with that amount if each tape measure costs $4.50?
22. Five more than three times a certain number is less than the number increased by thirteen. Find
the numbers that satisfy this condition.
23. Mark’s Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150.
For how many hours can you afford to rent the canoe?