Question

solve the inequality. then graph the solution set and write it in interval notation.\\(|2x + 2| \leq 6\\)\\(\dots\\)select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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 \(|2x + 2| \leq 6\), we get \(-6 \leq 2x + 2 \leq 6\).

Step2: Subtract 2 from all parts

Subtract 2 from each part of the compound inequality: \(-6 - 2 \leq 2x + 2 - 2 \leq 6 - 2\), which simplifies to \(-8 \leq 2x \leq 4\).

Step3: Divide by 2

Divide each part by 2: \(\frac{-8}{2} \leq \frac{2x}{2} \leq \frac{4}{2}\), resulting in \(-4 \leq x \leq 2\).

Answer:

The solution in interval notation is \([-4, 2]\)