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.

  • 4
    $\begingroup$ $|x|=|y|$ iff $x=\pm y$ $\endgroup$ – mrs Oct 14 '16 at 13:01
  • $\begingroup$ Split into the cases of $[x<0]$, $[0\leq x<\frac12]$ and $[\frac12\leq x]$. $\endgroup$ – barak manos Oct 14 '16 at 13:15
  • 1
    $\begingroup$ Suggest a sketch... $\endgroup$ – 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 $$-x=-2x+1$$

  • $\begingroup$ Thanks Dr. Graubner. Could you please explain further and moreover I don't get what you mean by "case work". Best Wishes, Obed. $\endgroup$ – Obed Antwi Oct 14 '16 at 16:06

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