Given the equation
$|x+2| + |3x+6| = 8,$
how can I find the sum of all its roots?
2026-03-26 19:35:55.1774553755
solving equation involving absolute values
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It's easy if you notice that $|3x+6| = 3|x+2|$.
So:
$\begin{align} |x+2| + |3x+6| &= 8 \\ |x+2| + 3|x+2| &= 8 \\ 4|x+2| &= 8 \\ |x+2| &= 2\end{align}$
Can you finish?