Solved Examples and Worksheet for Solving One-Step Linear Inequalities
Q1
Solve the inequality
- 10
a
≤ 50.
A
.
a
< 5
B
.
a
≤ - 5
C
.
a
> 5
D
.
a
≥ - 5
Solutions
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Step: 1
- 10
a
≤ 50
[Original equation.]
Step: 2
-
1
0
a
-
1
0
≥
5
0
-
1
0
[Divide each side by - 10 and reverse the direction of the inequality.]
Step: 3
a
≥ - 5
[Simplify.]
Correct Answer is :
a
≥ - 5
Q2
Solve the inequality
-8
b
> 56.
A
.
b
> -7
B
.
b
< -7
C
.
b
< 7
D
.
b
> 7
Solutions
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Step: 1
-8
b
> 56
[Original inequality.]
Step: 2
-8b
-8
<
56
-8
[Divide each side by -8 and reverse the inequality symbol.]
Step: 3
b
< -7
[Simplify.]
Correct Answer is :
b
< -7
Q3
Solve the inequality
- 6
k
≥ 30.
A
.
k
≥ 5
B
.
k
≤ 5
C
.
k
≥ - 5
D
.
k
≤ - 5
Solutions
Share
Step: 1
- 6
k
≥ 30
[Original inequality.]
Step: 2
-
6
k
-
6
≤
3
0
-
6
[Divide each side by - 6 and reverse the inequality symbol.]
Step: 3
k
≤ - 5
[Simplify.]
Correct Answer is :
k
≤ - 5
Q4
Simplify:
x
-5.7
≤ 12
A
.
x
≥ (-68.4)
B
.
x
≤ (-68.4)
C
.
x
< (-68.4)
D
.
x
> (-68.4)
Solutions
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Step: 1
x
-5.7
≤ 12
[Original inequality.]
Step: 2
-5.7x
-5.7
≥ 12 x (- 5.7)
[Multiply each side by - 5.7 and reverse the sign of the inequality.]
Step: 3
x
≥ (- 68.4)
[Simplify.]
Correct Answer is :
x
≥ (-68.4)
Q5
Which of the following inequalities is equivalent to
-
x
> - 5?
A
.
x
≤ 5
B
.
x
< 5
C
.
x
> 5
D
.
x
≥ 5
Solutions
Share
Step: 1
-
x
> -5
[Original inequality.]
Step: 2
-x
-1
<
-5
-1
[Divide by -1 on each side and reverse the inequality symbol.]
Step: 3
x
< 5
[Simplify.]
Step: 4
Among the choices, the inequality
x
< 5 is equivalent to -
x
> -5.
Correct Answer is :
x
< 5
Q6
Which of the following inequalities is equivalent to the inequality
15 > 3
j
?
A
.
j
> -5
B
.
j
≥ 5
C
.
j
≤ 5
D
.
j
< 5
Solutions
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Step: 1
15 > 3
j
[Original inequality.]
Step: 2
15
3
>
3j
3
[Divide each side by 3.]
Step: 3
j
< 5
[Simplify.]
Correct Answer is :
j
< 5
Q7
Solve the inequality.
1920 > 30
m
A
.
m
< 64
B
.
m
> 64
C
.
m
≥ 64
D
.
m
≤ 64
Solutions
Share
Step: 1
1920 > 30
m
[Original inequality.]
Step: 2
1920
30
>
30m
30
[Divide by 30 on each side.]
Step: 3
64 >
m
[Reverse the sign of the inequality.]
Step: 4
m
< 64
[Simplify.]
Correct Answer is :
m
< 64
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Related Topic
Inequality
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