# How do you solve the equation absx=x+3?

May 9, 2017

Use the definition:

|x|= {(x;x >=0),(-x;x < 0):}

#### Explanation:

Given: $\left\mid x \right\mid = x + 3$

Use the definition to break into two equations:

x = x+3; x >=0 and -x = x+3; x < 0

Subtract x from both sides of both equations:

0 = 3; x >=0 and -2x = 3; x < 0

Discard the first equation, because it can never be true:

-2x = 3; x < 0

Divide both sides by -2 and drop the restriction because it will obviously be true:

$x = - \frac{3}{2}$

Check:

$| - \frac{3}{2} | = - \frac{3}{2} + 3$

$\frac{3}{2} = \frac{3}{2}$

This checks

$x = - \frac{3}{2} \leftarrow$ answer.