Question

solve the following absolute value inequality:
$2|x + 2| - 8 > 14$
$square$ or $square$

Explanation:

Step1: Isolate absolute value term

Add 8 to both sides:
$2|x+2| - 8 + 8 > 14 + 8$
$2|x+2| > 22$

Step2: Simplify the inequality

Divide both sides by 2:
$\frac{2|x+2|}{2} > \frac{22}{2}$
$|x+2| > 11$

Step3: Split into two inequalities

For absolute value $|A| > B$, solve $A > B$ and $A < -B$:
$x+2 > 11$ and $x+2 < -11$

Step4: Solve first inequality

Subtract 2 from both sides:
$x+2 - 2 > 11 - 2$
$x > 9$

Step5: Solve second inequality

Subtract 2 from both sides:
$x+2 - 2 < -11 - 2$
$x < -13$

Answer:

$x < -13$ or $x > 9$