Example 3: Absolute Value Equations

Absolute Value

Example 3

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

Problem

\text{Greater solution of }|x-5|=4\text{ is }?

1. Recognize Pattern

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

2. Apply Method

|x-5|=7\Rightarrow x\in\left\{-2,12\right\}

3. Conclude

x=5\pm4\Rightarrow x\in\left\{1,9\right\}

Final answer

x=5\pm4\Rightarrow x\in\left\{1,9\right\}