Question

current learning objective: solving absolute value inequalities question 24 score: 0 of 1 point solve |3x + 2| < 1. give your answer as a compound inequality with integers or reduced fractions in the form a < x < b. solution: enter your answer √x submit answer attempts: 0/3 need help? mathgpt isnt available for this question, but you can still master it! if your instructor enabled practice similar questions, youll get unlimited practice opportunities, plus ai tutoring if also enabled. *ai ask mathgpt ai tutoring is no longer available for this assignment. licenses and credits

Explanation:

Step1: Rewrite absolute - value inequality

If \(|u| 0\)), then \(-a < u < a\). Here \(u = 3x + 2\) and \(a = 1\), so \(-1<3x + 2<1\).

Step2: Subtract 2 from all parts

\(-1-2<3x+2 - 2<1 - 2\), which simplifies to \(-3<3x<-1\).

Step3: Divide all parts by 3

\(\frac{-3}{3}<\frac{3x}{3}<\frac{-1}{3}\), resulting in \(-1 < x<-\frac{1}{3}\).

Answer:

\(-1 < x<-\frac{1}{3}\)