# Equation with absolute values and a parameter

I know how to solve equations with absolute values but without a parameter in the absolute value.

If "a" is a real and positive parameter

## |2x - 3a| + |a + 1 - x| = |x + 1|

But how can to approach this equation. I would be thankful for some tips and advice.

• Well, just consider cases $$x\ge / < \frac32a \\ x\le/>a+1 \\ x\ge/<-1$$ – user228113 Jul 6 '16 at 7:08
• Afterwards, you'll need to check for what values of $a$ the solutions you get agree with those conditions (which might contain a check of their consistency as well). – user228113 Jul 6 '16 at 7:11
• @G.Sassatelli Thank you. I was thinking something like that, but I was not sure cause I've never encountered an equation like this. Now it makes all perfect sense to me. Thank you very much :D – Gigaxel Jul 6 '16 at 7:21