Question

solve the following inequality algebraically. |x + 7| < 6

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|x + 7| < 6\), we have \(-6 < x + 7 < 6\).

Step2: Solve the left - hand inequality

Subtract 7 from both sides of \(-6 < x + 7\). We get \(-6-7 < x+7 - 7\), which simplifies to \(-13 < x\).

Step3: Solve the right - hand inequality

Subtract 7 from both sides of \(x + 7 < 6\). We get \(x+7 - 7<6 - 7\), which simplifies to \(x < - 1\).

Answer:

\(-13 < x < - 1\)