solve the following absolute value inequality. 6|x - 8| ≤ 12 x ≤ ? x ≥

Explanation:

Step1: Isolate the absolute - value expression

Divide both sides of the inequality $6|x - 8|\leq12$ by 6. We get $|x - 8|\leq2$. $$|x - 8|\leq2$$

Step2: Rewrite the absolute - value inequality as a compound inequality

If $|a|\leq b$ ($b\geq0$), then $-b\leq a\leq b$. So, $- 2\leq x - 8\leq2$.

Step3: Solve for $x$

Add 8 to all parts of the compound inequality: $-2 + 8\leq x-8 + 8\leq2 + 8$. $$6\leq x\leq10$$

Answer:

$x\leq10$; $x\geq6$