\(\left|2x-1\right|+\left|1-2x\right|=8\)
Vì \(2x-1\) và \(1-2x\) là hai số đối nhau.
\(\Rightarrow\left|2x-1\right|=\left|1-2x\right|.\)
\(\left|2x-1\right|+\left|1-2x\right|=8\)
\(\Rightarrow\left|2x-1\right|+\left|2x-1\right|=8\)
\(\Rightarrow2.\left|2x-1\right|=8\)
\(\Rightarrow\left|2x-1\right|=8:2\)
\(\Rightarrow\left|2x-1\right|=4.\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=4\\2x-1=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=5\\2x=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5:2\\x=\left(-3\right):2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{5}{2}\\x=-\frac{3}{2}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{5}{2};-\frac{3}{2}\right\}.\)
Chúc bạn học tốt!
