Question

select all the correct answers. which two inequalities can be used to find the soluti 3|x + 4| - 5 < 7 -3(x + 4) > 12 x + 4 < 4 x + 4 > -7 x + 4 > -4 3(x + 4) < -12 x + 4 < 7

Explanation:

Step1: Isolate the absolute value

Add 5 to both sides.
$3|x+4| - 5 + 5 < 7 + 5$
$3|x+4| < 12$

Step2: Simplify the inequality

Divide both sides by 3.
$\frac{3|x+4|}{3} < \frac{12}{3}$
$|x+4| < 4$

Step3: Rewrite as compound inequality

Apply absolute value rule $|A| < b \implies -b < A < b$.
$-4 < x+4 < 4$
This splits into $x+4 < 4$ and $x+4 > -4$.

Answer:

$x + 4 < 4$, $x + 4 > -4$