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

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SUMMARY

The equation |x + 3| = -6 has no real solutions because the absolute value of any expression is always non-negative. The definition of absolute value states that |u| is either u (when u is non-negative) or -u (when u is negative), ensuring that |u| is always greater than or equal to zero. Therefore, it is impossible for |x + 3| to equal a negative number like -6, confirming that no real numbers satisfy this equation.

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mathdad
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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:

$$0\le|u|$$ ?
 
https://mathhelpboards.com/pre-calculus-21/absolute-value-equation-22666.html
 

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