Question

question
solve the following inequality algebraically.
|x + 2| ≤ 12

Explanation:

Step1: Apply absolute value inequality rule

For $|A| \leq B$, this translates to $-B \leq A \leq B$. So:
$$-12 \leq x + 2 \leq 12$$

Step2: Subtract 2 from all parts

Isolate $x$ by subtracting 2 from each segment of the inequality:
$$-12 - 2 \leq x \leq 12 - 2$$

Step3: Simplify all terms

Calculate the resulting values:
$$-14 \leq x \leq 10$$

Answer:

$-14 \leq x \leq 10$