Question

Which inequality has 5 in its solution set?

a.) 5 - 2x is greater than or equal to 3
b.) 8 - 3x > -7
c.) 3x -4 is greater than or equal to 8
d.) 4 - 2x < -6

Answer 1

To find the inequality that has 5 in its solution set, we can substitute 5 into each inequality and see which one is true.

a.) 5 - 2x ≥ 3

Substituting 5:

5 - 2(5) ≥ 3

5 - 10 ≥ 3

-5 ≥ 3

This is not true.

b.) 8 - 3x > -7

Substituting 5:

8 - 3(5) > -7

8 - 15 > -7

-7 > -7

This is not true.

c.) 3x - 4 ≥ 8

Substituting 5:

3(5) - 4 ≥ 8

15 - 4 ≥ 8

11 ≥ 8

This is true.

d.) 4 - 2x < -6

Substituting 5:

4 - 2(5) < -6

4 - 10 < -6

-6 < -6

This is not true.

Therefore, the inequality that has 5 in its solution set is:

c.) 3x - 4 ≥ 8

Explanation: