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Worksheets

ABS Equ and Inequ

Total questions: 20

Worksheet time: 2hrs 40mins

Name
Class
Date
1.

Write an inequality for the graph.

a)

x<6x<6  

b)

x>6x>6  

c)

x6x\le6  

d)

x6x\ge6  

2.

Write an inequality for the graph.

a)

x<2x<-2

b)

x>2x>-2

c)

x2x\le-2

d)

x2x\ge-2

3.
Solve |2x –3| + 5 =10.
a)
-1, 1
b)
-1, 4
c)
-1, -4
d)
1, 4
4.
Solve |x – 12| - 3 = 11.
a)
-2, -26
b)
-2, 26
c)
3, 25
d)
4, -7
5.
∣ 2x + 9 ∣ = 15
a)
x = 3 
b)
x = 3
x = -6
c)
x = 3
x = -12
d)
x = 6
x = -12
6.

Solve.

|x + 4| < 5

a)

x < -9 or x > 1

b)

-9 < x < 1

c)

x < 9 or x > -1

d)

-1 < x < 9

7.
Solve.
|y - 4| ≥ 8
a)
y ≤ -4 or y ≥ 12
b)
-4 ≤ y ≤ -12
c)
y ≤ 4 or y ≥ -12
d)
-12 ≤ x ≤ 4
8.
Solve.
|y - 1| ≤ 6
a)
-7 ≤ y ≤ 5
b)
y ≤ -7 or y ≥ 5
c)
-5 ≤ y ≤ 7
d)
y ≤ -5 or y ≥ 7
9.
Solve.
|p + 3| ≥ 10
a)
-13 ≤ p ≤ 7
b)
p ≤ -13 or p ≥ 7
c)
-7 ≤ p ≤ 13
d)
p ≤ -7 or p ≥ 13
10.
Solve.
|2t + ⅔| < 4
a)
-5/3 < t < 7/3
b)
t > 7/3 or t < -5/3
c)
-7/3 < t < 5/3
d)
t > 5/3 or t < -7/3
11.

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

12.

Solve.

3|2d + 9| + 13 > 10

a)

d > 5 or d < -1

b)

d < -4 or d > 5

c)

No Solution

d)

All real numbers

13.
Solve.
|4m + 9| ≥ 21
a)
-7.5 ≤ m ≤ 3
b)
m ≤ -7.5 or m ≥ 3
c)
-3 ≤ m ≤ 7.5
d)
m ≤ -3 or m ≥ 7.5
14.
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
15.

x + 1 ≤ -3 or -4x < -8

a)

x ≤ -4 or x > 2

b)

x ≤ -4 and x > 2

c)

x ≤ -2 or x > 2

d)

x ≤ -2 and x > 2

16.

3 < 2x + 1 < 7

a)

1 < x < 3

b)

3 < x < 4

c)

3 < x < 3

d)

2 < x < 6

17.

26 ≤ 7n + 12 < 33

a)

2 ≤ n < 3

b)

3.7 ≤ n < 3

c)

5.4 ≤ n < 6.4

d)

4 ≤ n < 3

18.

Write the inequality statement.

a)

x > -14 and x < 4

b)

x > -14 or x < 4

c)

x ≥ -14 and x ≤ 4

d)

x ≥ -14 or x ≤ 4

19.

Write the inequality statement.

a)

x ≤ -3 or x > 2

b)

x ≤ -3 and x > 2

c)

x < -3 or x ≥ 2

d)

x < -3 and x ≥ 2

20.

The baseball team will spend $60 on new game balls for this season. They also want to purchase water bottles for $3 each. They have a budget of $1,000.


The inequality 3w + 60 ≤ 1000 models this scenario.


Which statement is true?

a)

The team can purchase 300 water bottles.

b)

The team can purchase 350 water bottles.

c)

The team can purchase 320 water bottles.

d)

The team can purchase 325 water bottles.