Question

solve the inequality graph the solution.
|2x + 3| - 14 ≤ -1

select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the solution is
(type an inequality or a compound inequality use integers or fractions for any numbers in the expression.)
b. the solution is all real numbers
c. there is no solution.

Explanation:

Step1: Isolate the absolute value

Add 14 to both sides:
$$|2x+3| - 14 + 14 \leq -1 + 14$$
$$|2x+3| \leq 13$$

Step2: Rewrite as compound inequality

For $|A| \leq b$, $-b \leq A \leq b$:
$$-13 \leq 2x+3 \leq 13$$

Step3: Subtract 3 from all parts

$$-13 - 3 \leq 2x+3 - 3 \leq 13 - 3$$
$$-16 \leq 2x \leq 10$$

Step4: Divide by 2 on all parts

$$\frac{-16}{2} \leq \frac{2x}{2} \leq \frac{10}{2}$$
$$-8 \leq x \leq 5$$

Answer:

A. The solution is $\boldsymbol{-8 \leq x \leq 5}$

(For the graph: Draw a number line, place closed circles at -8 and 5, and shade the region between these two points.)