Question

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

−5x − 7 < −22 and −5x − 7 ≥ −3
−5x − 7 > −22 and −5x − 7 ≥ −3
−5x > −22 and −7 ≥ −3
−5x − 7 < −22 and −5x − 7 ≤ −3

Answer 1

I believe it is the first one. Just split the original into 2 pieces and treat the inequality sign as an equal sign, but pay attention to which number or numbers the inequality is opened and closed to

Answer 2

The following which is an equivalent form of the compound inequality is:

`-5x-7<-22\ and\ -5x-7\geq -3`

Explanation:

We are given a compound inequality as:

`-22>-5x-7\geq -3`

The expression could also be written as:

First we take one of the inequality.

i.e.

`-22>-5x-7`

which is nothing but

`-5x-7<-22`

Then we take the other inequality as follows:

`-5x-7\geq -3`

Hence, the answer is:

`-5x-7<-22\ and\ -5x-7\geq -3`