Question

Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?

A. −5x − 7 < −22 and −5x − 7 ≥ −3

B. −5x − 7 > −22 and −5x − 7 ≥ −3

C. −5x > −22 and −7 ≥ −3

D. −5x − 7 < −22 and −5x − 7 ≤ −3

Answer 1

First, separate the given compound inequality a compound inequality written with the word "and".

\(−22 > −5x − 7 ≥ −3\)

\(-22 > -5x - 7\) and \(-5x - 7 \ge -3\)

Now look at the choices. There are several choices that have the right side above.
We need to work on the left side.
Keep in mind that if a > b, then b < a. Use this idea on the left side above.

Now change the left inequality above to:

-5x - 7 < -22

Now you have

\(-5x - 7 < -22\) and \(-5x - 7 \ge -3\)