-2
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Given the equation

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

how can I find the sum of all its roots?

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closed as off-topic by José Carlos Santos, John B, YiFan, Adrian Keister, Eevee Trainer Apr 6 at 0:17

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  • 1
    $\begingroup$ open absolute value bars $|x+2|=x+2$ if $x+2 \ge 0$ $\endgroup$ – Vasya Apr 5 at 10:57
  • $\begingroup$ Welcome to Math Stack Exchange. I edited the question to improve clarity; let me know if I deviated from your intent $\endgroup$ – J. W. Tanner Apr 5 at 12:33
3
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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?

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  • $\begingroup$ The one is 0 and the other is -4. So the answer is -4. Thanks $\endgroup$ – terrestrian Apr 5 at 11:01
  • $\begingroup$ Correct & you're welcome! $\endgroup$ – StackTD Apr 5 at 11:46

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