a)|x|+x=1/3
TH1: \(x+x=\dfrac{1}{3}\)
\(2x=\dfrac{1}{3}\)
\(x=\dfrac{1}{3}:2\)
\(x=\dfrac{1}{6}\)
TH2: -x+x=1/3
0=1/3 ( ko thõa mãn )
Vậy x=1/6
b) |x|-x=3/4
TH1: x-x=3/4
0=3/4 (ko thõa mãn)
TH2: \(-x-x=\dfrac{3}{4}\)
\(-2x=\dfrac{3}{4}\)
\(x=\dfrac{3}{4}:\left(-2\right)\)
\(x=\dfrac{3}{-8}=-\dfrac{3}{8}\)
Vậy x=-3/8
c) |x-2|=x
TH1: x-2=x
2=x-x
2=0 ( ko thõa mãn)
TH2: -(x-2)=x
-x+2=x
2=-x-x
2=-2x
x=-2:2
x=-1
Vậy x=-1
B (Erik): Bạn làm thiếu trường hợp câu a nhé!
a) \(\left|x\right|+x=\dfrac{1}{3}\Leftrightarrow\left\{{}\begin{matrix}x+x=\dfrac{1}{3}\\x+x=-\dfrac{1}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=\dfrac{1}{3}\\2x=-\dfrac{1}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{6}\\x=-\dfrac{1}{6}\end{matrix}\right.\)
b) \(\left|x\right|-x=\dfrac{3}{4}\Leftrightarrow-x-x=\dfrac{3}{4}\Leftrightarrow-2x=\dfrac{3}{4}\Leftrightarrow x=-\dfrac{3}{8}\)
c) \(\left|x-2\right|=x\Leftrightarrow\left\{{}\begin{matrix}x-2=x\\x-2=-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-x=2\\x+x=2\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}0=2\\2x=2\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}x\in\varnothing\\x=1\end{matrix}\right.\)