# How do you solve the equation abs(x-3)=5?

May 23, 2017

See explanation.

#### Explanation:

The absolute value of an expression is $5$ if the expression's value is either $5$ or $- 5$, so this absolute value equation can be changed to 2 equations without absolute value.

$| x - 3 | = 5 \iff x - 3 = 5 \vee x - 3 = - 5$

If you solve the 2 equations you get:

$x - 3 = 5 \implies x = 8$

and

$x - 3 = - 5 \implies x = - 2$

The equation has 2 solutions: $x = - 2$ and $x = 8$