a) \(\left|x-2\right|=3\) (1)
\(\left|x-2\right|=x-2\Leftrightarrow x-2\ge0\Leftrightarrow x\ge2\)
\(\left|x-2\right|=2-x\Leftrightarrow x-2< 0\Leftrightarrow x< 2\)
*) Với \(x\ge2\)
(1) \(\Leftrightarrow x-2=3\)
\(\Leftrightarrow x=5\) (nhận)
*) Với \(x< 2\)
(1) \(\Leftrightarrow2-x=3\)
\(\Leftrightarrow-x=3-2\)
\(\Leftrightarrow-x=1\)
\(\Leftrightarrow x=-1\) (nhận)
Vậy S = {\(-1;5\)}
b) \(\left|x-3\right|=2x-5\) (2)
\(\left|x-3\right|=x-3\Leftrightarrow x-3\ge0\Leftrightarrow x\ge3\)
\(\left|x-3\right|=3-x\Leftrightarrow x-3< 0\Leftrightarrow x< 3\)
*) Với \(x\ge3\)
(2) \(\Leftrightarrow x-3=2x-5\)
\(\Leftrightarrow2x-x=-3+5\)
\(\Leftrightarrow x=2\) (loại)
*) Với \(x< 3\)
(2) \(\Leftrightarrow3-x=2x-5\)
\(\Leftrightarrow2x+x=3+5\)
\(\Leftrightarrow3x=8\)
\(x=\dfrac{8}{3}\) (nhận)
Vậy \(S=\left\{\dfrac{8}{3}\right\}\)
c) \(\left|-2x\right|=3x+4\) (3)
\(\left|-2x\right|=-2x\Leftrightarrow-2x\ge0\Leftrightarrow x\le0\)
\(\left|-2x\right|=2x\Leftrightarrow-2x< 0\Leftrightarrow x>0\)
*) Với \(x\le0\)
(3) \(\Leftrightarrow-2x=3x+4\)
\(\Leftrightarrow-2x-3x=4\)
\(\Leftrightarrow-5x=4\)
\(\Leftrightarrow x=-\dfrac{4}{5}\) (nhận)
*) Với \(x>0\)
(3) \(\Leftrightarrow2x=3x+4\)
\(\Leftrightarrow2x-3x=4\)
\(\Leftrightarrow-x=4\)
\(\Leftrightarrow x=-4\) (loại)
Vậy \(S=\left\{-\dfrac{4}{5}\right\}\)
