Example 5: Absolute Value Equations

Absolute Value

Example 5

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

Problem

\text{Greater solution of }|x--3|=5\text{ is }?

1. Recognize Pattern

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

2. Apply Method

|x-7|=2\Rightarrow x\in\left\{5,9\right\}

3. Conclude

x=-3\pm5\Rightarrow x\in\left\{-8,2\right\}

Final answer

x=-3\pm5\Rightarrow x\in\left\{-8,2\right\}