Question

Which of the following is an equivalent form of the compound inequality: -44 > -2x -8 ≥ -8?

B) -2x > -44 and -8 ≥ -8
C) -2x -8 < -44 and -2x - 8 (less than sign) -8
D) -2x - 8 < -44 and -2x - 8 ≥ -8

Already tried A so I left that out since that answer was wrong. Please, provide step by steps on how you got your answer.

Answer 1

If you read the inequality from center to left you get -2x - 8 < -44 then from center to the right it is -2x - 8 >= -8 you get D.

Answer is choice D.

Answer 2

D) -2x - 8 < -44 and -2x - 8 ≥ -8

Explanation:

The given inequality is

`-44>-2x-8\geq -8`

Every compound inequality can be expressed as two inequalities

`-44>-2x-8\\-2x-8\geq -8`

Observe that the first inequality is equal to

`-2x-8<-44`

It represents the same.

Therefore, the separated inequalities are

`-2x-8<-44`

`-2x-8\geq -8`

Therefore, the right asnwer is D., those are the inequalities which are equivalent to the given compound inequality.