Question

5-|2x-1|=x

Answer 1

\(5-\left|2x-1\right|=x\)

\(\Leftrightarrow\left|2x-1\right|=5-x\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5-x\\2x-1=-\left(5-x\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5-x\\2x-1=-5+x\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+x=5+1\\2x-x=-5+1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3x=6\\x=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\)

Answer 2

=>|2x-1|=5-x

TH1: x>=1/2

=>2x-1=5-x

=>3x=6

=>x=2(nhận)

TH2: x<1/2

=>1-2x=5-x

=>-x=4

=>x=-4(nhận)