Question

Solve the following equation |x – 3| = 4. Show all work.

Answer 1

x=7, x=−1

Explaination

Find all solutions for x

by breaking the absolute value into the positive and negative components.

Answer 2

Solving Equations with Absolute Values

Answer:

`x = 7` and
`x = -1`

Explanation:

Solving for the Positive Absolute Value:

`|x -3| = 4 \\ x -3 = 4 \\ x -3 +3 = 4 +3 \\ x = 7`

Solving for the Negative Absolute Value:

`|x -3| = 4 \\ -(x -3) = 4 \\ -(x -3) \cdot -1 = 4 \cdot -1 \\ x -3 = -4 \\ x -3 +3 = -4 +3 \\ x = -1`