Question

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

Answer 1

`x=5`

Explanation:

Since `5-x = -(x-5)`, 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 \iff |x-5|`

which ultimately leads to `x-5=0 \implies x=5`