Question

solve the absolute value inequality. - 7|x - 5|≥ - 28
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in interval notation is
(simplify your answer.)
b. the solution set is ∅.

Explanation:

Step1: Divide both sides by -7

When dividing an inequality by a negative number, the inequality sign flips. So we have $|x - 5|\leq4$.

Step2: Rewrite as compound - inequality

We rewrite $|x - 5|\leq4$ as $- 4\leq x - 5\leq4$.

Step3: Solve for x

Add 5 to all parts of the compound - inequality: $-4 + 5\leq x-5 + 5\leq4 + 5$, which simplifies to $1\leq x\leq9$.

Answer:

A. The solution set in interval notation is $[1,9]$