Question

Tìm x biết: 2.|5x-3|-2x=14

Answer 1

\(2\left|5x-3\right|-2x=14\)

xét th1: \(5x-3\ge0\Leftrightarrow5x\ge3\Leftrightarrow x\ge\dfrac{3}{5}\)

thì \(2\left|5x-3\right|-2x=14\) \(\Leftrightarrow\) \(2\left(5x-3\right)-2x=14\Leftrightarrow10x-6-2x=14\)

\(\Leftrightarrow8x=20\Leftrightarrow x=\dfrac{20}{8}\) (tmđk)

th2: \(5x-3< 0\Leftrightarrow5x< 3\Leftrightarrow x< \dfrac{3}{5}\)

thì \(2\left|5x-3\right|-2x=14\) \(\Leftrightarrow2\left(3-5x\right)-2x=14\Leftrightarrow6-10x-2x=14\)

\(\Leftrightarrow-12x=8\Leftrightarrow x=\dfrac{-8}{12}=\dfrac{-2}{3}\) (tmđk)

vậy \(x=\dfrac{20}{8};x=\dfrac{-2}{3}\)