How do you solve abs(1/2x-3)=2?

Mar 3, 2018

See explanation.

Explanation:

First we have to change the equation with absolute value to a set of 2 equations without absolute value.

$| \frac{1}{2} x - 3 | = 2$

is equivalent to:

$\frac{1}{2} x - 3 = 2 \vee \frac{1}{2} x - 3 = - 2$

Now we can solve the both equations:

$\frac{1}{2} x = 5 \vee \frac{1}{2} x = 1$

$x = 10 \vee x = 2$