Question

Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6?

Answer 1

ANSWER

$9\: < x \leqslant0$

EXPLANATION

The given compound inequality is

$- 33 \: > - 3x - 6 \geqslant - 6$

We need to simplify this inequality so that we can obtain x standing alone between the inequality signs.

We add 6 through out the inequality.

$- 33 + 6\: > - 3x - 6 + 6 \geqslant - 6 + 6$

This simplifies to:

$- 27\: > - 3x \geqslant 0$

We now divide through by -3 and reverse the inequality sign.

$\frac{- 27}{ - 3} \: < \frac{ - 3x}{ - 3} \leqslant \frac{0}{ - 3}$

We now simplify to get:

$9\: < x \leqslant 0$