Download Algebra Chapter 3 Review Answer Key

Name
Class
Date
Chapter 3 Review
ANSWER KEY
Write an inequality that represents each verbal expression or graph.
1. all real numbers n that are less than –3 .
n < -3
4z ≥ 7
2. The product of 4 and z is greater than or equal to 7.
3.
4.
x≥2
x<1
Circle each number that is a solution of the given inequality.
4y + 3 ≤ –7
a. –3
b. –1
6. –6x + 2 > 5
a. –3
b. 4
5.
Solve each inequality. Graph the solutions.
7. 6m + 1 ≤ 3m – 8
m ≤ -3 (graph should have a solid
dot on -3 and an arrow to the left.)
9.
b
3

c. 3
1
2
c. –0.5 (a and b are solutions)
8. 4(3w – 1) ≥ 20
w ≥ 2 (graph should have a solid
dot on 2 and an arrow to the right)
>
b > -12 (graph should have an open circle on -12 and an arrow to the right.)
Solve each inequality, if possible. If the inequality has no solution, write
no solution. If the solutions are all real numbers, write all real numbers.
10. 8n – 20 < 4(2n – 5)
11. 4d – 9 ≤ 6d + 15
8n – 20 < 8n – 20
8n < 8n
n<n
no solution – a number can’t
be less than itself.
12. 5t – 6 – 3t ≤ 2(t – 2)
2t – 6 ≤ 2t – 4 or
2t ≤ 2t + 2
t≤t+1
All real numbers
-9 ≤ 2d +15
-24 ≤ 2d
-12 ≤ d
d ≥ -12
13. 8 – 7x > 15
2t – 6 ≤ 2t – 4
-6 ≤ – 4
(always true)
-7x > 7
x < -1
14. Sharon earns $25 per item she sells plus a base salary of $100 per week. Write and
solve an inequality to find how many items she must sell to earn at least $700 per week.
Let x = number of items she sells
100 + 25x ≥ 700
25x ≥ 600
x ≥ 24
Sharon must sell at least 24 items.
15. A class is raising funds for a field trip. The candy sale brought in $127 the first week
and $178 the second week. The class would like to raise $500. Write and solve an
inequality to describe how much money the class needs to bring in
the next week to exceed their goal.
Let d = dollars earned next week
127 + 178 + d > 500
305 + d > 500
d > 195
The class must bring in more than $195.
16. Error Analysis A student claims that the graph below represents the solution of the
inequality 5x – 7 < 13. What error did the student make? What should
the graph of the solution be?
The student should have put an open circle on 4.
Write a compound inequality that each graph could represent.
17.
18.
-1 ≤ x < 3
x < 0 OR x > 2
Solve and graph each compound inequality.
19. 4 < n + 7 ≤ 12
20. –1 ≤ –4k ≤ 8
-3 < n ≤ 5
The graph should have an open
circle on -3 and a closed dot on 12,
with shading between the two.
21. 4y < –24 or 6y > 12
-1≤ -4k and
-4k ≤ 8
¼≥k
k ≥ -2
k≤¼
k ≥ -2
-2 ≤ k ≤ ¼
The graph has a closed dot on -2 and a
closed dot on ¼, with shading between
the two.
22. –2p ≤ –18 or 3p < 9
p ≥ 9 or p < 3
The graph has an open circle on
3, with shading to the left, and a
closed dot on 9, with shading to the right.
y < -6 or y > 2
The graph has an open circle on
-6, with shading to the left,
and an open circle on 2, with
shading to the right.
Solve each equation or inequality. If there is not a solution, write no solution.
23.
|x| = 5
x = 5 or -5
24.
|a + 2| > 4
a + 2 > 4 a + 2 < -4
a > 2 OR a < -6
25. |3z – 6| = 9
26.
3z – 6 = 9 or 3z – 6 = -9
3z = 15
or 3z = -3
z=5
or z = -1
|v + 4| ≤ 10
v + 4 ≤ 10 or v + 4 ≥ -10
v≤6
or v ≥ -14
-14 ≤ v ≤ 6
27. Which of the following inequalities could be represented by the graph? (This is Ms. Simpson’s
favorite question, BTW.)
I.
|n
– 1| < 2
n – 1 < 2 or n – 1 > -2
n<3
n > -1
YES
II. 4x < 12 or –x < 2
x<3
or x > -2
NO
III. 1 < 3h + 4 < 13
-3 < 3h < 9
-1 < h < 3
YES
A. I only
B. I and II
C. II and III
D. I and III
28. Open-Ended Write an absolute value inequality that has 3 and –6 as two of
its solutions.
Many possible answers. Two ways to approach it:
1) An “AND” inequality where -6 and 3 are between the endpoints. For example, -7 ≤ x
≤ 7. This would translate to |x| ≤ 7.
2) An “OR” inequality such as |x+2| ≥ 3. (Solutions for this would be x ≥ 1 or x ≤ -5.
29. Writing Explain why |4x| + 7 = 2 has no solution.
When you subtract 7 from both sides of the equation, the result is |4x| = -5.
Absolute value can never be negative, so there is no solution.