Example 6: Absolute Value Equations

Absolute Value

Example 6

Step-by-step worked example for this lesson track.

Problem

\text{Greater solution of }|x-2|=5\text{ is }?

1. Recognize Pattern

|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

|x--10|=2\Rightarrow x\in\left\{-12,-8\right\}

3. Conclude

x=2\pm5\Rightarrow x\in\left\{-3,7\right\}

Final answer

x=2\pm5\Rightarrow x\in\left\{-3,7\right\}