Question

select the correct answer. what is the solution to |x - 7| ≥ 1? 6 ≤ x ≤ 8; -8 ≤ x ≤ -6; x ≥ -6 or x ≤ -8; x ≥ 8 or x ≤ 6

Explanation:

Step1: Split absolute value inequality

For $|x-7| \geq 1$, this translates to two cases:
$x-7 \geq 1$ or $x-7 \leq -1$

Step2: Solve first inequality

Isolate $x$ by adding 7 to both sides.
$x-7+7 \geq 1+7$
$x \geq 8$

Step3: Solve second inequality

Isolate $x$ by adding 7 to both sides.
$x-7+7 \leq -1+7$
$x \leq 6$

Answer:

x ≥ 8 or x ≤ 6