# How do you solve  3x+5=abs(x-6)?

Mar 14, 2018

$x = 0.25$

#### Explanation:

Because of the absolute value function ($\left\mid \right\mid$), the function inside can be positive or negative.

$3 x + 5 = x - 6$ or $3 x + 5 = 6 - x$

$2 x = - 11$ or $4 x = 1$

$x = - \frac{11}{2} \mathmr{and} \frac{1}{4}$

Now to check:
$3 \left(0.25\right) + 5 = \frac{23}{4}$
$\left\mid 0.25 - 6 \right\mid = \frac{23}{4}$

$3 \left(- \frac{11}{2}\right) + 5 = - \frac{23}{2}$
$\left\mid - \frac{11}{2} - 6 \right\mid = \frac{23}{2}$

So, $x = 0.25$