Question

Tìm x:

a) \(\left|4x+3\right|-x=15\)

Answer 1

\(\left|4x+3\right|-x=15\)

th1: \(4x+3\ge0\Leftrightarrow4x\ge-3\Leftrightarrow x\ge\dfrac{-3}{4}\)

\(\Rightarrow\left|4x+3\right|-x=15\Leftrightarrow4x+3-x=15\Leftrightarrow4x-x=15-3\)

\(\Leftrightarrow3x=12\Leftrightarrow x=\dfrac{12}{3}=4\left(tmđk\right)\)

th2: \(4x+3< 0\Leftrightarrow4x< -3\Leftrightarrow x< \dfrac{-3}{4}\)

\(\Rightarrow\left|4x+3\right|-x=15\Leftrightarrow-\left(4x+3\right)-x=15\Leftrightarrow-4x-3-x=15\)

\(\Leftrightarrow-4x-x=15+3\Leftrightarrow-5x=18\Leftrightarrow x=\dfrac{-18}{5}\left(tmđk\right)\)

vậy \(x=4;x=\dfrac{-18}{5}\)