Question

solve the absolute inequality. then graph the solution set on a number line.
|2p + 8| ≤ 6
progress: 0/2
part 1 of 2
solve the absolute inequality as much as possible. if there is no solution, click on
o solution\. if the solution is all real numbers, click on \all reals\.

Explanation:

Step1: Apply absolute value inequality rule

For \(|A| \leq B\) (where \(B\geq0\)), it is equivalent to \(-B \leq A \leq B\). So for \(|2p + 8| \leq 6\), we get \(-6 \leq 2p + 8 \leq 6\).

Step2: Subtract 8 from all parts

Subtract 8 from each part of the compound inequality: \(-6 - 8 \leq 2p + 8 - 8 \leq 6 - 8\), which simplifies to \(-14 \leq 2p \leq -2\).

Step3: Divide by 2

Divide each part by 2: \(\frac{-14}{2} \leq \frac{2p}{2} \leq \frac{-2}{2}\), resulting in \(-7 \leq p \leq -1\).

Answer:

\(-7 \leq p \leq -1\)