Why does |x + 3| = -6 have no real solutions?

[mathdad]

Explain why there are no real numbers that
satisfy the equation | x + 3 | = - 6.

I know the reason is because of the negative number. Why is this the case?

 

[MarkFL]

Let's look at a definition:

$$|u|=\begin{cases}u, & 0\le u \\[3pt] -u, & u<0 \\ \end{cases}$$

Can you see that we must have:

$$0\le|u|$$ ?

 

[skeeter]

https://mathhelpboards.com/pre-calculus-21/absolute-value-equation-22666.html