Question

solve the following inequality algebraically.
|x - 8| > 6

Explanation:

Step1: Apply absolute value rule

For $|A| > B$, this translates to $A > B$ or $A < -B$. So:
$x - 8 > 6$ or $x - 8 < -6$

Step2: Solve first inequality

Isolate $x$ by adding 8 to both sides:
$x - 8 + 8 > 6 + 8$
$x > 14$

Step3: Solve second inequality

Isolate $x$ by adding 8 to both sides:
$x - 8 + 8 < -6 + 8$
$x < 2$

Answer:

$x < 2$ or $x > 14$ (in interval notation: $(-\infty, 2) \cup (14, \infty)$)