Question

Tìm x biết: | 2x-3 | - x = | 2-x |

Giải chi tiết giùm nhe!

Answer 1

\(\left|2x-3\right|-x=\left|2-x\right|\)

TH1 \(\left\{{}\begin{matrix}2x-3\ge0\\2-x\ge0\end{matrix}\right.\Leftrightarrow\dfrac{3}{2}\le x\le2\)

\(\Leftrightarrow2x-3-x=2-x\Leftrightarrow x=\dfrac{5}{2}\left(l\right)\)

TH2 \(\left\{{}\begin{matrix}2x-3\ge0\\2-x\le0\end{matrix}\right.\Leftrightarrow x\ge2\)

\(\Leftrightarrow2x-3-x=x-2\Leftrightarrow0=1\left(vl\right)\)

Th3 \(\left\{{}\begin{matrix}2x-3\le0\\2-x\ge0\end{matrix}\right.\Leftrightarrow x\le\dfrac{3}{2}\)

\(\Leftrightarrow3-2x-x=x-2\Leftrightarrow x=\dfrac{5}{4}\left(nhận\right)\)

TH4 \(\left\{{}\begin{matrix}2x-3\le0\\2-x\le0\end{matrix}\right.\left(vl\right)\)

vậy \(S=\left\{\dfrac{5}{4}\right\}\)