Question

How do you solve this equation: -2m+3=|15+m|

Answer 1

Any number inside the modulus sign becomes positive. This means $|15+m|=|-(15+m)|=|-15-m|$ and so we have,

$-2m+3=|15+m| \Rightarrow \left \Big\{ {{-2m+3=15+m} \atop{-2m+3=-15-m}} \right$

Solving these gives us

$-2m+3=15+m \Rightarrow m=-4$

$-2m+3=-15-m \Rightarrow = m=18$

However if we check the second solution in the original equation we obtain $-2(18)+3=|15+18| \Rightarrow -33=33$. This is false and so $m=18$ can't be a solution.

Therefore the only solution is $m=-4$.

(Note: I'm not sure why the second solution didn't work but when there's a modulus sign involved it always pays to check your final answers to be sure. I'll have a think about it but in case you find out before I do, I'd be interested to know in the comments.)