Linear Equations And Inequalities In One Variable Worksheet With Answer Key Page 6
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8(2-61)
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2.9 Solving Inequalities and Applications
2 . 9
E X E R C I S E S
Reading and Writing After reading this section, write out the
19. 8
2b
b
4
answers to these questions. Use complete sentences.
1. What are equivalent inequalities?
20. 35
7b
b
5
Equivalent inequalities are inequalities that have the same
solutions.
21.
4z
8
z
2
2. What is the addition property of inequality?
The addition property of inequality says that adding any
22.
5y
20
y
4
real number to each side of an inequality produces an
equivalent inequality.
23. 3y
2
7
y
3
3. What is the multiplication property of inequality?
According to the multiplication property of inequality, the
inequality symbol is reversed when multiplying (or divid-
24. 2y
5
9
y
2
ing) by a negative number and not reversed when multiply-
ing (or dividing) by a positive number.
25. 3
7z
17
z
2
4. What similarities are there between solving equations and
solving inequalities?
26. 5
3z
20
z
5
For equations or inequalities we try to isolate the variable.
The properties of equality and inequality are similar.
5. How do we solve compound inequalities?
27. 6
r
3
r
3
We solve compound inequalities using the properties of in-
equality as we do for simple inequalities.
28. 6
12
r
r
6
6. How do you know when to reverse the direction of an in-
equality symbol?
29. 5
4p
8
3p
The direction of the inequality symbol is reversed when we
p
13
multiply or divide by a negative number.
30. 7
9p
11
8p
Write the appropriate inequality symbol in the blank so that the
p
4
two inequalities are equivalent. See Example 1.
5
31.
q
20
q
24
7. x
7
0
8. x
6
0
6
x ___
7
x ___ 6
x
7
x
6
2
32.
q
4
q
6
9. 9
3w
10. 10
5z
3
w ___ 3
z ___ 2
1
w
3
z
2
33. 1
t
2
t
12
4
11.
4k
4
12.
9t
27
k ___ 1
t ___ 3
1
34. 2
t
0
t
6
k
1
t
3
3
1
1
13.
y
4
14.
x
4
35. 2x
5
x
6
x
11
2
3
y ___
8
x ___
12
y
8
x
12
36. 3x
4
2x
9
x
13
Solve and graph each of the following inequalities. See Exam-
ples 2 and 3.
37. x
4
2(x
3)
x
10
15. x
3
0
x
3
38. 2x
3
3(x
5)
x
18
16. x
9
8
x
17
39. 0.52x
35
0.45x
8
x
614.3
17.
3
w
1
w
2
40. 8455(x
3.4)
4320
18. 9
w
12
w
21
x
3.91
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