Example 9: Absolute Value Equations

Absolute Value

Example 9

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

Problem

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

1. Recognize Pattern

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

2. Apply Method

|x-10|=3\Rightarrow x\in\left\{7,13\right\}

3. Conclude

x=5\pm5\Rightarrow x\in\left\{0,10\right\}

Final answer

x=5\pm5\Rightarrow x\in\left\{0,10\right\}