# Solutions to an equation.

How many solutions exist to the equation $|x|=|2x - 1|$?

I just don't know where to start from, so I humbly need your help.

• $|x|=|y|$ iff $x=\pm y$ – mrs Oct 14 '16 at 13:01
• Split into the cases of $[x<0]$, $[0\leq x<\frac12]$ and $[\frac12\leq x]$. – barak manos Oct 14 '16 at 13:15
• Suggest a sketch... – coffeemath Oct 14 '16 at 13:27

Hnt: you must do case work: a) $$x\geq \frac{1}{2}$$ and we have to solve $$x=2x-1$$ b) $$0\le x <\frac{1}{2}$$ thus we get $$x=-2x+1$$ c)$$x<0$$ and we have to solve $$-x=-2x+1$$