a, Với mọi giá trị của x ta có:
\(\left|2x+3\right|+\left|-x-1\right|\ge0\)
mà \(\left|2x+3\right|+\left|-x-1\right|=5x\)
nên \(5x\ge0\Rightarrow x\ge0\)
\(\Rightarrow\left\{{}\begin{matrix}2x+3>0\\-x-1< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left|2x+3\right|=2x+3\\\left|-x-1\right|=x+1\end{matrix}\right.\)
\(\Rightarrow2x+3+x+1=5x\)
\(\Rightarrow5x-2x-x=4\Rightarrow2x=4\Rightarrow x=2\)
Vậy.............
b,
Với mọi giá trị của x ta có:
\(\left|-3-2x\right|+\left|x+5\right|\ge0\)
mà \(\left|-3-2x\right|+\left|x+5\right|=2x\)
nên \(2x\ge0\Rightarrow x\ge0\)
\(\Rightarrow\left\{{}\begin{matrix}-3-2x< 0\\x+5< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left|-3-2x\right|=3+2x\\\left|x+5\right|=x+5\end{matrix}\right.\)
\(\Rightarrow3+2x+x+5=2x\)
\(\Rightarrow2x-2x-x=5+3\Rightarrow-x=8\Rightarrow x=-8\)
Vậy...........
Chúc bạn học tốt!!!
\(\left|2x+3\right|+\left|-x+1\right|=5x\)
\(\left|2x+3\right|\ge0;\left|-x+1\right|\ge0\)
\(\Rightarrow\left|2x+3\right|+\left|-x+1\right|\ge0\Rightarrow5x\ge0\)
\(\Rightarrow2x+3-x+1=5x\)
\(\Rightarrow x+4=5x\Rightarrow4x=4\Rightarrow x=1\)
\(\left|-3-2x\right|+\left|x+5\right|=2x\)
\(\left|-3-2x\right|\ge0;\left|x+5\right|\ge0\)
\(\Rightarrow\left|-3-2x\right|+\left|x+5\right|\ge0\Rightarrow2x\ge0\)
\(\Rightarrow-3-2x+x+5=2x\)
\(2-x=2x\)
\(\Rightarrow3x=2\Rightarrow x=\dfrac{2}{3}\)
