Name:_______________________
Algebra II: Absolute Value Equations and Inequalities:
Homework #6
Directions: On the following worksheet, do problems 1-30. Write all work
neatly and readably on separate sheets of paper, and write the final answers
to each problem in space provided on the worksheet. For all inequalities,
write the answer in interval notation.
This worksheet can be found and used free of charge at
http://www.conceptsapplications.com/comb_2/chapters/comb9_3.pdf
EXTRA PRACTICE 25
Solving Equations and Inequalities With Absolute Value
Use after Section 9.3
Name_______________________________
__________________________________________________________________
Examples: Solve.
a)
3x − 5 = 16
b)
3x − 5 = − 16 or 3 x − 5 = 16
3x = − 11 or
x=−
11
or
3
− 16 ≤ 3x − 5 ≤ 16
3x = 21
− 11 ≤ 3x ≤ 21
x=7
−
 11 
The solution set is − ,7  .
 3 
c)
3x − 5 ≤ 16
11
≤x≤7
3
11


The solution set is x − ≤ x ≤ 7 .
3


3x − 5 > 16
3x − 5 < −16 or 3x − 5 > 16
3x < −11 or
x<−
11
or
3
3 x > 21
x >7
11


The solution set is x x < −
or x > 7 .
3


Solve.
1.
8x − 3 > 21
______________
2.
y −2 ≤ 7
______________
3.
5x + 8 < 23
______________
4.
9 − 2x = 5
______________
5.
x =4
______________
6.
1
y−3 ≥3
2
______________
7.
y +9 ≤ 2
______________
8.
y+
9.
− 4 x + 3 > 13
______________
10.
1
4
>
3
3
5
x < 10
8
Copyright ©1998 Addison Wesley Longman, Inc.
______________
______________
EXTRA PRACTICE 25
Solving Equations and Inequalities With Absolute Value
Use after Section 9.3
__________________________________________________________________
11.
10 y − 1.3 = 4.7
______________
12.
9 − 4x ≥ 15
______________
13.
x + 9 > 17
______________
14.
3
1
+x =
4
4
______________
15.
9 − y > 11
______________
16.
y ≤
1
5
______________
17.
3
3
y >
7
7
______________
18.
3− x = 2
______________
19.
5x − 2 ≥ 15
______________
20.
17 − 4 x < 23
______________
21.
y − 3 = 51
______________
22.
19 − x > 19
______________
23.
8x − 3 ≤ 5
______________
24.
2 y − 9 < 15
______________
25.
y >9
______________
26.
3y −
5
4
≤
9
9
______________
27.
8 − 3y < 35
______________
28.
0.2 x + 0.5 ≥ 0.9 ______________
29.
x−
______________
30.
34 − 4 y ≤ 14
2
4
≥
9
9
Copyright ©1998 Addison Wesley Longman, Inc.
______________