# How do you solve |x - 10| = 20?

Dec 14, 2016

$x = 30 \text{ or } x = - 10$

#### Explanation:

The $\textcolor{b l u e}{\text{absolute value}}$ is always positive. This is because it gives a measure of how far a value is from zero, irrespective of it's sign.

$\text{That is } | - 4 | = | 4 | = 4$

$\Rightarrow | x - 10 | = 20 \text{ has 2 solutions}$

$x - 10 = 20 \textcolor{red}{\text{ or }} - \left(x - 10\right) = 20$

• x-10=20rArrx=30color(red)" or"

•-x+10=20rArr-x=10rArrx=-10

$\textcolor{b l u e}{\text{As a check}}$

$| 30 - 10 | = | 20 | = 20 \text{ and } | - 10 - 10 | = | - 20 | = 20$