Question

solve the following inequality algebraically.\\(|x + 8| < 8\\)

Explanation:

Step1: Apply absolute value rule

For $|A| < b$ (where $b>0$), rewrite as $-b < A < b$.
So we get: $-8 < x + 8 < 8$

Step2: Subtract 8 from all parts

Subtract 8 to isolate $x$.

$$\begin{align*} -8 - 8 &< x + 8 - 8 < 8 - 8 \\ -16 &< x < 0 \end{align*}$$

Step3: Write in interval notation

Express the inequality as an interval.
$(-16, 0)$

Answer:

$(-16, 0)$