a) \(\left|4+2x\right|=-4x\)
th1: \(4+2x\ge0\Leftrightarrow2x\ge-4\Leftrightarrow x\ge\dfrac{-4}{2}=-2\)
\(\Rightarrow\left|4+2x\right|=-4x\Leftrightarrow4+2x=-4x\Leftrightarrow4=-4x-2x=-6x\)
\(\Leftrightarrow x=\dfrac{4}{-6}=\dfrac{-2}{3}\left(tmđk\right)\)
th2: \(4+2x< 0\Leftrightarrow2x< -4\Leftrightarrow x< \dfrac{-4}{2}=-2\)
\(\Rightarrow\left|4+2x\right|=-4x\Leftrightarrow-4-2x=-4x\Leftrightarrow-4=-4x+2x=-2x\)
\(\Leftrightarrow x=\dfrac{-4}{-2}=2\left(loại\right)\)
vậy \(x=\dfrac{-2}{3}\)
b) \(\left|3x-1\right|+2=x\)
th1: \(3x-1\ge0\Leftrightarrow3x\ge1\Leftrightarrow x\ge\dfrac{1}{3}\)
\(\Rightarrow\left|3x-1\right|+2=x\Leftrightarrow3x-1+2=x\Leftrightarrow3x-x=1-2\)
\(\Leftrightarrow2x=-1\Leftrightarrow x=\dfrac{-1}{2}\left(loại\right)\)
th2: \(3x-1< 0\Leftrightarrow3x< 1\Leftrightarrow x< \dfrac{1}{3}\)
\(\Rightarrow\left|3x-1\right|+2=x\Leftrightarrow1-3x+2=x\Leftrightarrow x+3x=1+2\)
\(\Leftrightarrow4x=3\Leftrightarrow x=\dfrac{3}{4}\left(loại\right)\)
vậy phương trình vô nghiệm
c) \(\left|x+15\right|+1=3x\)
th1: \(x+15\ge0\Leftrightarrow x\ge-15\)
\(\Rightarrow\left|x+15\right|+1=3x\Leftrightarrow x+15+1=3x\Leftrightarrow3x-x=15+1\)
\(\Leftrightarrow2x=16\Leftrightarrow x=\dfrac{16}{2}=8\left(tmđk\right)\)
th2: \(x+15< 0\Leftrightarrow x< -15\)
\(\Rightarrow\left|x+15\right|+1=3x\Leftrightarrow-x-15+1=3x\Leftrightarrow3x+x=-15+1\)
\(\Leftrightarrow4x=-14\Leftrightarrow x=\dfrac{-14}{4}=\dfrac{-7}{2}\left(loại\right)\)
vậy \(x=8\)
d) \(\left|2x-5\right|+x=2\)
th1: \(2x-5\ge0\Leftrightarrow2x\ge5\Leftrightarrow x\ge\dfrac{5}{2}\)
\(\Rightarrow\left|2x-5\right|+x=2\Leftrightarrow2x-5+x=2\Leftrightarrow2x+x=2+5\)
\(\Leftrightarrow3x=7\Leftrightarrow x=\dfrac{7}{3}\left(loại\right)\)
th2: \(2x-5< 0\Leftrightarrow2x< 5\Leftrightarrow x< \dfrac{5}{2}\)
\(\Rightarrow\left|2x-5\right|+x=2\Leftrightarrow5-2x+x=2\Leftrightarrow-2x+x=2-5\)
\(\Leftrightarrow-x=-3\Leftrightarrow x=3\left(loại\right)\)
vậy phương trình vô nghiệm