Question

Solve absolute value equation. Check for extraneous solution. |2x-3|=2x-1. Post it into the drop box for the unit 2 review.

Answer 1

let's keep in mind that, an absolute value expression is in effect a piecewise one, since it has a ± versions of it.

$\bf |2x-3|=2x-1\implies \begin{cases}+(2x-3)=2x-1\\-(2x-3)=2x-1\end{cases}\\\\[-0.35em]~\dotfill\\\\+(2x-3)=2x-1\implies 2x-3=2x-1\implies -3 \ne -1\impliedby extraneous\\\\[-0.35em]~\dotfill\\\\-(2x-3)=2x-1\implies 2x-3=-2x+1\implies 4x=4\\\\\\x=\cfrac{4}{4}\implies x=1$