#### Solved Examples and Worksheet for Solving One-Step Linear Inequalities

Q1Solve the inequality - 10a ≤ 50.

A. a < 5
B. a ≤ - 5
C. a > 5
D. a ≥ - 5

Step: 1
- 10a ≤ 50
[Original equation.]
Step: 2
- 10a- 1050- 10
[Divide each side by - 10 and reverse the direction of the inequality.]
Step: 3
a ≥ - 5
[Simplify.]
Correct Answer is :   a ≥ - 5
Q2Solve the inequality -8b > 56.
A. b > -7
B. b < -7
C. b < 7
D. b > 7

Step: 1
-8b > 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
Q3Solve the inequality - 6k ≥ 30.
A. k ≥ 5
B. k ≤ 5
C. k ≥ - 5
D. k ≤ - 5

Step: 1
- 6k ≥ 30
[Original inequality.]
Step: 2
- 6k- 630- 6
[Divide each side by - 6 and reverse the inequality symbol.]
Step: 3
k ≤ - 5
[Simplify.]
Correct Answer is :   k ≤ - 5
Q4Simplify: x-5.7 ≤ 12

A. x ≥ (-68.4)
B. x ≤ (-68.4)
C. x < (-68.4)
D. x > (-68.4)

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)
Q5Which of the following inequalities is equivalent to -x > - 5?

A. x ≤ 5
B. x < 5
C. x > 5
D. x ≥ 5

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
Q6Which of the following inequalities is equivalent to the inequality 15 > 3j?

A. j > -5
B. j ≥ 5
C. j ≤ 5
D. j < 5

Step: 1
15 > 3j
[Original inequality.]
Step: 2
153 > 3j3
[Divide each side by 3.]
Step: 3
j < 5
[Simplify.]
Correct Answer is :   j < 5
Q7Solve the inequality. 1920 > 30m
A. m < 64
B. m > 64
C. m ≥ 64
D. m ≤ 64

Step: 1
1920 > 30m
[Original inequality.]
Step: 2
192030 > 30m30
[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