Question

solve the following compound inequality.
-6 ≤ 3x - 9 ≤ 3

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solutions are
(simplify your answer. type an inequality or a compound inequality.)

b. the solutions are all real numbers.

c. there is no solution.

Explanation:

Step1: Add 9 to all parts

To solve the compound inequality \(-6 \leq 3x - 9 \leq 3\), we first add 9 to each part of the inequality. This is done to isolate the term with \(x\).
Adding 9 to each part: \(-6 + 9 \leq 3x - 9 + 9 \leq 3 + 9\)
Simplifying each part: \(3 \leq 3x \leq 12\)

Step2: Divide all parts by 3

Next, we divide each part of the inequality by 3 to solve for \(x\). Dividing by a positive number does not change the direction of the inequality signs.
Dividing each part by 3: \(\frac{3}{3} \leq \frac{3x}{3} \leq \frac{12}{3}\)
Simplifying each part: \(1 \leq x \leq 4\)

Answer:

A. The solutions are \(1 \leq x \leq 4\)