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

May 12, 2018

$x = 5$

#### Explanation:

Since $5 - x = - \left(x - 5\right)$, you have $| x - 5 | = | 5 - x |$. In fact, the absolute value will always consider the positive version of the number. For example, $| - 5 | = | 5 | = 5$. or $| - 2 | = | 2 | = 2$.

So, in general, $| x | = | - x |$ holds.

The equation becomes

$| x - 5 | = - | x - 5$

and thus

$2 | x - 5 | = 0 \setminus \iff | x - 5 |$

which ultimately leads to $x - 5 = 0 \setminus \implies x = 5$