Question

question
what is the solution of the following inequality?
|5x + 7| < 7

answer attempt 1 out of 3
○ {x|x < -14/5 or x > 0} ○ {x|x < 0 or x > 14/5}
○ {x|0 < x < 14/5} ○ {x| -14/5 < x < 0}

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| < B\) (where \(B>0\)), it is equivalent to \(-B < A < B\). So for \(|5x + 7| < 7\), we have \(-7 < 5x + 7 < 7\).

Step2: Subtract 7 from all parts

Subtract 7 from each part of the compound inequality: \(-7 - 7 < 5x + 7 - 7 < 7 - 7\), which simplifies to \(-14 < 5x < 0\).

Step3: Divide by 5

Divide each part by 5: \(\frac{-14}{5} < \frac{5x}{5} < \frac{0}{5}\), so \(-\frac{14}{5} < x < 0\).

Answer:

\(\{x|-\frac{14}{5} < x < 0\}\)