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2.6 Absolute Value Inequalities Review of AND

Total questions: 10

Worksheet time: 47mins

Name
Class
Date
1.
Solve.
|c + 4| < 5
a)
x < -9 or x > 1
b)
-9 < x < 1
c)
x < 9 or x > -1
d)
-1 < x < 9
2.
Solve.
|y - 1| ≤ 6
a)
-7 ≤ y ≤ 5
b)
y ≤ -7 or y ≥ 5
c)
-5 ≤ y ≤ 7
d)
y ≤ -5 or y ≥ 7
3.
Solve.
|3c - 4| < 12
a)
-2 2/3 < c < 5 1/3
b)
c < -5 1/3  or c > 2 2/3
c)
c < 5 1/3 or c > -2 2/3
d)
-5 1/3 < c < 2 2/3
4.
Solve.
3|d - 4| = 12
a)
d = -8 or d = 0
b)
no solution
c)
d = 8 or d = 0
d)
d = 40 or d = 32
5.
Solve.
6 - 2|m -3| > -4
a)
-8 < m < 2
b)
m < -8 or m > 2
c)
m < -2 or m > 8
d)
-2 < m < 8
6.

A golf ball manufacturer puts 390 golf balls in each box. The box can be off by 6 golf balls. Write an inequality that displays the acceptable amount of golf balls that can be in a box.

a)

|x - 6| < 390

b)

|x - 6| ≤ 390

c)

|x - 390| < 6

d)

|x - 390| ≤ 6

7.

Caleb is a machinist at Golden Eagle Chopper Shop. To ensure the reliability of the motorcycle engines produced at the shop, Caleb machines each cylinder to a 4.01mm diameter with a tolerance of 0.002mm. Write an absolute value inequality to determine if a cylinder’s diameter is acceptable.

a)

|x - 0.002| ≤ 4.01

b)

|x - 4.01| ≤ 0.002

c)

|x - 4.01| < 0.002

d)

|x + 4.01| ≤ 0.002

8.

3 < 2x + 1 < 7

a)

1 < x < 3

b)

3 < x < 4

c)

3 < x < 3

d)

2 < x < 6

9.

2x + 9 < 7 or -5x + 7 < -8

a)

x < -1 or x > 3

b)

x < 8 or x > 3

c)

x < -1 and x > 3

d)

x < 8 and x > 3

10.
Write an inequality for Graph 3.
a)
x ≤ -2 AND x > 5
b)
x ≤ -2 OR x > 5
c)
x ≥ -2 OR x < 5
d)
-2 ≤ x < 5