# solving equation involving absolute values [closed]

Given the equation

$$|x+2| + |3x+6| = 8,$$

how can I find the sum of all its roots?

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• open absolute value bars $|x+2|=x+2$ if $x+2 \ge 0$ – Vasya Apr 5 at 10:57
• Welcome to Math Stack Exchange. I edited the question to improve clarity; let me know if I deviated from your intent – J. W. Tanner Apr 5 at 12:33

It's easy if you notice that $$|3x+6| = 3|x+2|$$.
\begin{align} |x+2| + |3x+6| &= 8 \\ |x+2| + 3|x+2| &= 8 \\ 4|x+2| &= 8 \\ |x+2| &= 2\end{align}