MHB Explaining the Absence of Real Solutions for |x + 3| = -6

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The equation |x + 3| = -6 has no real solutions because the absolute value of any real number is always non-negative. This means that |u| is defined to be either u or -u, resulting in |u| being greater than or equal to zero. Since -6 is negative, it cannot equal the absolute value of any expression. Therefore, there are no real numbers that satisfy the equation. The fundamental property of absolute values confirms this conclusion.
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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?
 
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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:

$$0\le|u|$$ ?
 
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