# How do you solve abs(x-5) = abs(x+5) ?

Mar 3, 2017

$x = 0$

#### Explanation:

Given:

$\left\mid x - 5 \right\mid = \left\mid x + 5 \right\mid$

We can square both sides of the equation, solve the resulting equation, then check the solution...

Squaring both sides we get:

$\textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{2}}}} - 10 x + \textcolor{red}{\cancel{\textcolor{b l a c k}{25}}} = \textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{2}}}} + 10 x + \textcolor{red}{\cancel{\textcolor{b l a c k}{25}}}$

Subtract ${x}^{2} + 25$ from both sides to get:

$- 10 x = 10 x$

Add $10 x$ to both sides to get:

$0 = 20 x$

Divide both sides by $20$ and transpose to get:

$x = 0$

Check:

$\left\mid \textcolor{b l u e}{0} - 5 \right\mid = 5 = \left\mid \textcolor{b l u e}{0} + 5 \right\mid$