1. Tìm \(x\) biết:
a. \(\left|x\right|\)= \(x+2\) với \(x+2\) \(\ge\) 0
b. \(\left|1-3x\right|=x-7\) với \(x-7\) \(\ge\) 0
c. \(\left|2x-3\right|+5-x\) với \(x-5\) \(\le\) 0
2. Tìm \(x\) biết:
a. \(\left|x-\dfrac{3}{2}\right|=\left|\dfrac{5}{2}-x\right|\)
b. \(\left|x-1\right|+\left|x-4\right|=3x\)
c. \(\left|x-\dfrac{3}{2}\right|+\left|\dfrac{-5}{3}+x\right|=0\)
d. \(\left|x.\left(x-4\right)\right|=x\)
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1) |x|=x+2
=> \(\left[{}\begin{matrix}x=x+2\\x=-x-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}0=2\left(voli\right)\\2x=-2\Rightarrow x=-1\end{matrix}\right.\)
vậy x=-1
c;b tương tự
2) \(\left|x-\dfrac{3}{2}\right|=\left|\dfrac{5}{2}-x\right|\)
=> \(\left[{}\begin{matrix}x-\dfrac{3}{2}=\dfrac{5}{2}-x\\x-\dfrac{3}{2}=x-\dfrac{5}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=4\Rightarrow x=2\\0=-1\left(voli\right)\end{matrix}\right.\)
vậy x=2
