Why isn't the definition of absolute value applied when squaring a radical containing a variable? I recently learned about the following definition of absolute value:

$|a| = \sqrt{a^2}$

Then I came across a solution to a problem that had the following step:

$5 \geq \sqrt{5 - x}$

In order to proceed, we had to square both sides:

$5^2 \geq (\sqrt{5 - x})^2$

With the aforementioned definition of absolute value in mind, I wrote:

$25 \geq |5 - x|$

But the actual solution turned out to be:

$25 \geq 5 - x$

I don't understand why the absolute value definition wasn't applied here. Can anyone tell me why?

From the fact that you can take $\sqrt {5-x}$ you know that $5-x \ge 0$ so you don't need the absolute value signs.
