# How do you solve the equation abs(6-2x)=6?

May 2, 2018

As shown below:

#### Explanation:

Absolute values can only be positive, so the first step i solving this equations, is to find the region where the values of $x$ is negative, and the values of $x$ are positive.

Achieve this like so:

$2 x = - 1 \implies x = - \frac{1}{2}$

Therefore

Now you have two equations you have to solve:

$6 = - 6 + 2 x$

$6 = 6 - 2 x$

$x = 0 , x = 6$

If you're in a hurry, (or slightly lazy like I am), you can always enter the equation into your graphing calculator, like this:

y = abs(6+2x), y = 6, and (if you're using a Ti 83 or 84) press

(2nd) --> {calc} ---> intersect

Hope it helps!