Question

Tìm x, biết:

a, \(|2x-3|-\dfrac{5}{2}=\dfrac{1}{3}\)

b, \(|x-1|+3x=1\)

c, \(|5x-3|-x=7\)

d, \(|2x+1|+|x+8|=4x\)

e, \(|3x+2|+|4x+3|=2x-4\)

f, \(|2x-4|+|8-4x|=15\)

g, \(|x^2-2x|=x\)

Answer 1

a) \(\left|2x-3\right|-\dfrac{5}{2}=\dfrac{1}{3}\)

\(\left|2x-3\right|=\dfrac{1}{3}+\dfrac{5}{2}=\dfrac{2}{6}+\dfrac{15}{6}\)

\(\left|2x-3\right|=\dfrac{17}{6}\)

\(+)2x-3=\dfrac{17}{6}\Rightarrow2x=\dfrac{35}{6}\Rightarrow x=\dfrac{35}{12}\)

\(+)2x-3=\dfrac{-17}{6}\Rightarrow2x=\dfrac{1}{6}\Rightarrow x=\dfrac{1}{12}\)

vậy...

Answer 2

\(\left|x-1\right|+3x=1\\ \Rightarrow\left|x-1\right|=1-3x\\ \Rightarrow\left\{{}\begin{matrix}x-1=1-3x\\x-1=-1+3x\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}4x=2\\-2x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\x=0\end{matrix}\right.\)

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