Question

question
solve the following inequality algebraically.
|x + 10| < 2

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). Here, \(a = x + 10\) and \(b = 2\), so we get \(-2 < x + 10 < 2\).

Step2: Solve the compound inequality

Subtract 10 from all parts of the inequality: \(-2 - 10 < x + 10 - 10 < 2 - 10\).
Simplify each part: \(-12 < x < -8\).

Answer:

\(-12 < x < -8\)