Question

question
what is the solution of the following inequality?
|5x + 11| < 6

answer attempt 1 out of 3
{ x | x < 1 or x > 17/5 } { x | 1 < x < 17/5 }
{ x | x < -17/5 or x > -1 } { x | -17/5 < x < -1 }

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| < B\) (where \(B>0\)), it is equivalent to \(-B < A < B\). So for \(|5x + 11| < 6\), we have \(-6 < 5x + 11 < 6\).

Step2: Subtract 11 from all parts

Subtract 11 from each part of the compound inequality: \(-6 - 11 < 5x + 11 - 11 < 6 - 11\). This simplifies to \(-17 < 5x < -5\).

Step3: Divide by 5

Divide each part by 5: \(\frac{-17}{5} < \frac{5x}{5} < \frac{-5}{5}\). Which simplifies to \(-\frac{17}{5} < x < -1\).

Answer:

\(\{x|-\frac{17}{5} < x < -1\}\)