Question

question
solve the following inequality algebraically.
$5|x + 8| - 7 < 13$

Explanation:

Step1: Isolate the absolute value term

Add 7 to both sides:
$5|x + 8| - 7 + 7 < 13 + 7$
$5|x + 8| < 20$

Step2: Simplify the inequality

Divide both sides by 5:
$\frac{5|x + 8|}{5} < \frac{20}{5}$
$|x + 8| < 4$

Step3: Rewrite without absolute value

For $|A| < B$ ($B>0$), $-B < A < B$:
$-4 < x + 8 < 4$

Step4: Solve for x

Subtract 8 from all parts:
$-4 - 8 < x + 8 - 8 < 4 - 8$
$-12 < x < -4$

Answer:

$-12 < x < -4$