Question

What solution value satisfies the compound inequality 4 < 3x∕2 + 1 < 7?

Answer 1

Answer:

C) x = 3

Step-by-step explanation:

To find the solution value that satisfies the inequality 4 < 3x∕2 + 1 < 7, you must plug every x value into the x and see which one works.

Plug 0 into x

4 < 3(0)∕2 + 1 < 7

4 < 0∕2 + 1 < 7

4 < 0 + 1 < 7

Combine like terms

4 < 1 < 7

This is false, 1 is not greater than 4.

Plug 4 into x

4 < 3(4)∕2 + 1 < 7

4 < 12∕2 + 1 < 7

4 < 6 + 1 < 7

Combine like terms

4 < 7 < 7

This is false, 7 is not less than 7.

Plug 3 into x.

4 < 3(3)∕2 + 1 < 7

4 < 9∕2 + 1 < 7

4 < 4.5 + 1 < 7

Combine like terms

4 < 5.5 < 7

This is true, 5.5 is greater than 4 and less than 7.

Plug 6 into x.

4 < 3(6)∕2 + 1 < 7

4 < 18∕2 + 1 < 7

4 < 9 + 1 < 7

Combine like terms

4 < 10 < 7

This is false, 10 is not less than 7.

C) x = 3 is the only true solution that works, so that is your answer.

I hope that helped and have a lovely rest of your day! :)