Question

solve the absolute value inequality. |3x - 3| < 12 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: Rewrite absolute - value inequality

Recall that \(|a|\lt b\) is equivalent to \(-b\lt a\lt b\). So, \(|3x - 3|\lt12\) is equivalent to \(- 12\lt3x - 3\lt12\).

Step2: Add 3 to all parts

Adding 3 to each part of the compound - inequality \(-12\lt3x - 3\lt12\) gives \(-12 + 3\lt3x-3 + 3\lt12 + 3\), which simplifies to \(-9\lt3x\lt15\).

Step3: Divide all parts by 3

Dividing each part of \(-9\lt3x\lt15\) by 3, we get \(\frac{-9}{3}\lt\frac{3x}{3}\lt\frac{15}{3}\), which simplifies to \(-3\lt x\lt5\).

Step4: Write in interval notation

The solution in interval notation is \((-3,5)\).

Answer:

A. The solution set in interval notation is \((-3,5)\)