Question

tìm x

2 \(\left|x-1\right|\) - 3x = 7

Answer 1

\(2\left|x-1\right|-3x=7\)

th1: \(x-1\ge0\Leftrightarrow x\ge1\)

\(\Rightarrow2\left|x-1\right|-3x=7\Leftrightarrow2\left(x-1\right)-3x=7\Leftrightarrow2x-2-3x=7\)

\(\Leftrightarrow2x-3x=7+2\Leftrightarrow-x=9\Leftrightarrow x=-9\left(loại\right)\)

th2: \(x-1< 0\Leftrightarrow x< 1\)

\(\Rightarrow2\left|x-1\right|-3x=7\Leftrightarrow2\left(1-x\right)-3x=7\Leftrightarrow2-2x-3x=7\)

\(\Leftrightarrow-2x-3x=7-2\Leftrightarrow-5x=5\Leftrightarrow x=-1\left(tmđk\right)\) vậy \(x=-1\)