# How do you solve abs(x-1)+17=6?

Apr 2, 2015

There is no value of $x$ to satisfy this equation.

$\left\mid x - 1 \right\mid = - 11$

As we know, absolute value will always return a non-negative value.

Such that:

$\mathmr{if} c \ge 0 , \left\mid c \right\mid = c$

$\mathmr{if} c < 0 , \left\mid c \right\mid = - c$

So either way the right-hand part of the equation where the absolute value is equal to is always be positive (or zero).

Since $- 11$ is a negative number, there is no such $x$ to satisfy the equation because absolute value will never be equal to a negative number.

The result is: $x \in \left\{\right\}$