Why can't $|x-2|$ be less than zero? Just confused with the concepts in Absolute Value.
So we know that to solve absolute value equations such,
$$|x-2| = 5 \tag1$$
In this case we have, $x-2 = 5$ and $x-2 = -5$. then solve for $x$.
However,
$$|x-2| = -5 \tag2$$
Here is no solution.

Why can't the absolute value be less than zero?

Is it from a graph that we cannot get negative values from the $y$-axis? Are there any other explanations?
A proof is highly appreciated.

By definition we have,$$|x|=\begin{cases}x&\text{ if }x\geqslant0\\-x&\text{ if }x<0,\end{cases}$$and therefore we always have $|x|\geqslant0$.
In order to solve the equation $|x-2|=5$ you can consider two possibilities:

*

*$x\geqslant2$. Then $|x-2|=5$ is the same thing as $x-2=5$. So, $x=7$.

*$x<2$. Then $|x-2|=5$ is the same thing as $-(x-2)=5$. So, $x=-3$.

