Question

if \\(|x + 5| \leq 6\\), then \\(a \leq 2x - 8 \leq b\\). find \\(a\\) and \\(b\\).\\(a = \square\\) (simplify your answer.)

Explanation:

Step1: Rewrite absolute value inequality

$-6 \leq x + 5 \leq 6$

Step2: Isolate $x$ (subtract 5)

$-6 - 5 \leq x \leq 6 - 5$
$-11 \leq x \leq 1$

Step3: Multiply all terms by 2

$2\times(-11) \leq 2x \leq 2\times1$
$-22 \leq 2x \leq 2$

Step4: Subtract 8 from all terms

$-22 - 8 \leq 2x - 8 \leq 2 - 8$
$-30 \leq 2x - 8 \leq -6$

Answer:

$a = -30$, $b = -6$