Question

question
what is the solution of the following inequality?
|3x + 2| < 8

answer attempt 1 out of 3
{ x|x < -10/3 or x > 2 } { x|x < -2 or x > 10/3 }
{ x| -2 < x < 10/3 } { x| -10/3 < x < 2 }

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|3x + 2| < 8\), we have \(-8 < 3x + 2 < 8\).

Step2: Solve the left - hand inequality

Subtract 2 from all parts of the compound inequality: \(-8 - 2<3x+2 - 2<8 - 2\), which simplifies to \(-10 < 3x<6\).

Step3: Solve for x

Divide all parts of the inequality by 3: \(\frac{-10}{3}<\frac{3x}{3}<\frac{6}{3}\), which gives \(-\frac{10}{3}

Answer:

\(\{x|-\frac{10}{3}