# How do you solve |x + 3| = (x-2)?

Apr 14, 2017

No solution

#### Explanation:

Since absolute values are always nonnegative,

$| x + 3 | = x - 2 \ge q 0 R i g h t a r r o w x \ge q 2$,

which means that $x + 3$ is nonnegative.

So, the equation becomes (by simply removing the absolute value sign)

$R i g h t a r r o w x + 3 = x - 2$

By subtracting $x$ from both sides,

$R i g h t a r r o w 3 = - 2$,

which is false.

Hence, there is no solution.

I hope that this was clear.

Apr 14, 2017

No real solution.

#### Explanation:

We have

$\left\mid x + 3 \right\mid = x + 3 - 5$ or assuming $x \ne - 3$

$1 = \frac{x + 3}{\left\mid x + 3 \right\mid} - \frac{5}{\left\mid x + 3 \right\mid}$ so there are two possibilities

$\left\{\begin{matrix}1 = 1 - \frac{5}{\left\mid x + 3 \right\mid} \\ 1 = - 1 - \frac{5}{\left\mid x + 3 \right\mid}\end{matrix}\right.$

and in both cases there is not a real solution for the equations.