Name:_________________________________
Period:_____________
Date:______
Chapter 3: Inequalities Test REVIEW SHEET
Complete the following questions. Show all work in the space provided. Do not answer a question without
providing an explanation or some work – even on multiple-choice!!
1) Given the following set of words.
A) At most
B) At least
C) No more than
D) No less than
E) More than
F) Less than
G) Greater than or equal to
H) Less than or equal to
Which statement is true?
(1) The symbol > can be written as A and G only
(3) The symbol < can be written as A and C only
(2) The symbol > can be written as B and D only
(4) The symbol < can be written as A, C, and H
2) Write an inequality shown on the accompanying
graph in set-builder and interval notation.
3
5) Which inequality is equivalent to 9 > 2 𝑥 − 6?
(1) x < 7
(2) x < 2
(3) 𝑥 < 8
(4) x < 10
3) Which value of x is in the solution set of:
4
𝑥 + 5 < 17
3
6) Find all negative odd integers that satisfy the
following inequality:
−3𝑥 + 1 ≤ 17
(1) 8
(2) 9
(3) 12
(4) 16
4) The inequality 3𝑥 + 2 > 𝑥 + 8 is the same as
3
(1) 𝑥 > − 2
3
(2) 𝑥 > 2
(3) 𝑥 > 3
(4) 𝑥 < 3
7) Which value of x is in the solution set of
-4x + 2 > 10?
(1) -2
(2) 2
(3) 3
(4) -4
8) Graph the conjunction (𝑥 < 4) and (𝑥 ≥ −13) and 13) Which of the following inequalities is not
write it in set-builder notation.
equivalent to 𝑥 < −3?
9) The statement “The sum of twice a number and 18 is
greater than 25” can be expressed as
(1)
(2)
(3)
(4)
2𝑛 + 18 = 25
2(𝑛 + 18) > 25
2(𝑛 + 18) > 50
2𝑛 + 18 > 25
10) The length of a rectangle is 15 and its width is w.
The perimeter of the rectangle is, at most 50. Which
inequality can be used to find the longest possible
width?
(1) 30 + 2𝑤 ≤ 50
(2) 30 + 2𝑤 < 50
(3) 30 + 2𝑤 ≥ 50
(4) 30 + 2𝑤 > 50
(1) 𝑥 + 2 < −1
(2) 𝑥 − 4 < −7
(3) 2𝑥 < −6
(4) −3𝑥 > 9
(5) all are equivalent
14) Bob has four more than twice as many CDs as Jim.
If they have a total of 31 CDs, how many CDs does
Jim have?
(1)
(2)
(3)
(4)
22
14
13
9
15) Solve:
|
2𝑥−1
3
|=5
11) If x is a member of the set of integers, the solution
set of −4 < 𝑥 ≤ 1 is
(1) {-4, -3, -2, 0}
(2) {-3, -2, -1, 0, 1}
(3) {-4, -3, -2, 0, 1}
(4) {-3, -2, 0}
12) Graph the disjunction (𝑥 < −2) ⋁ (𝑥 > 3)
and write it in set notation.
16) The manufacturer of Ron’s car recommends that the tire
pressure be at least 26 pounds per square inch and less than
35 pounds per square inch. Create a number line and graph the
inequality that represents the recommended tire pressure. Then
write a compound inequality that represents the recommended tire
pressure.
17) Solve the inequality below algebraically for x.
Graph, and then write your answer in interval and
set-builder notation.
−3 − 6(4𝑥 + 6) ≤ −111
21) Solve, graph, and write the solution set in
interval notation:
−18 < 2𝑥 − 4 < 6
18) Solve, graph and write solution in set-builder
notation:
|3 – 2x| > 4
22) Solve and graph the inequality. Write your
answer in interval notation.
2
− 3 (−9𝑥 + 12) ≥ 12 − 2𝑥
19) Thelma and Laura start a lawn-mowing business and buy a
lawnmower for $225. They plan to charge $15 to mow one
lawn. What is the minimum number of lawns they need to
mow if they wish to earn a profit of at least $750?
23) The heights, h, of the students in the chorus at Central
Middle School satisfy the inequality below, when h is
measured in inches. Determine the interval in which these
heights lie and express your answer in set-builder notation.
ℎ − 57.5
|
| ≤ 3.25
2
20) Frank is going to buy some ties at $7.50 per tie and some
shirts at $18.50 per shirt. If he buys twice as many ties as
shirts and spends no more than $205, what is the greatest
number of shirts he can buy? [All prices include tax.]
24) Mark used the formula 𝐷 = 𝑟𝑡 to determine how long it
should take him to drive 275 miles at 55 miles per hour. He
got 220 hours for his answer. Explain his error and how to get
the correct answer.
Chapter 3 Review Sheet Answers:
1. 4
2. [−1, ∞); {𝑥|𝑥 ≥ −1}
3. 1
4. 3
5. 4
6. -5, -3, -1
7. 4
8. {x| -13 < x < 4}
9. 4
10. 1
11. 2
12. {x| x < -2 or x > 3}
13. 5
14. 4
15. {-7, 8}
16. 26 < p < 35
17. [3, ∞), {𝑥|𝑥 ≥ 3}
1
7
18. {𝑥|𝑥 ≤ − 2 𝑜𝑟 𝑥 ≥ 2}
19. 65
20. 6 shirts
21. (-7, 5)
22. [2.5, ∞)
23. {h| 51 < h < 64}
24. The correct answer is 5. Provide an explanation of what Mark did wrong.