# How do you solve the equation abs(x-a)=b?

May 5, 2017

$x = a + b$ or $x = a - b$ if $b \ge 0$.

#### Explanation:

$| x - a | = b$ means that

either $x - a = b$ i.e. $x = a + b$

or $x - a = - b$ i.e. $x = a - b$

Note that as absolute value of any number is always $0$ or positive, hence we should have $b \ge 0$ and if $b < 0$, there is no solution.