Question

question
solve the following inequality algebraically.
|x - 2| < 12

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|x - 2| < 12\), we can rewrite it as \(-12 < x - 2 < 12\).

Step2: Solve the compound inequality

Add 2 to all parts of the inequality: \(-12 + 2 < x - 2 + 2 < 12 + 2\).
Simplify each part: \(-10 < x < 14\).

Answer:

The solution to the inequality \(|x - 2| < 12\) is \(-10 < x < 14\)