Question

solving a compound inequality. check all that apply.

Answer 1

Answer:

The solutions are:

-28.25, -14.5, -2.25

Step-by-step explanation:

Given compound inequality is:

$-17.5\leq \frac{2x+4}{3} <17.5$

The compound inequalities are broken down into two inequalities to find the solution

The two inequalities will be:

$\frac{2x+4}{3} \geq -17.5$   AND   $\frac{2x+4}{3}<{17.5}$

Solving both inequalities one by one

$\frac{2x+4}{3} \geq -17.5\\2x+4 \geq -52.5\\2x \geq -52.5-4\\2x \geq -56.5\\\frac{2x}{2} \geq \frac{-56.5}{2}\\x \geq -28.25\\\frac{2x+4}{3} < 17.5\\2x+4 < 52.5\\2x < 52.5-4\\2x \geq 48.5\\\frac{2x}{2} \geq \frac{48.5}{2}\\x < 24.25$

The solution is:

-28.25 ≤ x < 24.25

We have to see which options lie in the solution range.

The solutions are:

-28.25, -14.5, -2.25