Question

question
solve the following inequality algebraically.
$4|x - 8| - 2 < 18$

Explanation:

Step1: Isolate the absolute value term

Add 2 to both sides of the inequality:
$4|x-8| - 2 + 2 < 18 + 2$
$4|x-8| < 20$

Step2: Simplify the inequality

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

Step3: Rewrite without absolute value

For $|A| < B$ (where $B>0$), this translates to $-B < A < B$:
$-5 < x - 8 < 5$

Step4: Solve for x

Add 8 to all parts of the compound inequality:
$-5 + 8 < x - 8 + 8 < 5 + 8$
$3 < x < 13$

Answer:

$3 < x < 13$