Question

Giải các phương trình sau :

a) |x - 1| - 2x = 3

b) 1/2 . |2 - x| = 2x - 1

Answer 1

Ek bải giải này bạn gì ơi!!!

a) \(\left|x-1\right|-2x=3\) \(\Leftrightarrow\left|x-1\right|=3+2x\)

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

Vậy S=\(\left\{-4;\dfrac{-2}{3}\right\}\)

b) \(\dfrac{1}{2}.\left|2-x\right|=2x-1\Leftrightarrow\left|2-x\right|=\dfrac{2x-1}{\dfrac{1}{2}}\)

\(\Leftrightarrow\left|2-x\right|=2.\left(2x-1\right)\)\(\Leftrightarrow\left\{{}\begin{matrix}2-x=4x-2\Leftrightarrow x=\dfrac{4}{5}\\2-x=-4x+2\Leftrightarrow x=0\end{matrix}\right.\)

Vậy S=\(\left\{0;\dfrac{4}{5}\right\}\)

Answer 2

a) |x-1| -2x = 3 <=> |x-1| = 3+2x

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

Vậy..........

b) \(\dfrac{1}{2}\left|2-x\right|=2x-1\Leftrightarrow\left|2-x\right|=4x-2\)

\(\Leftrightarrow\left[{}\begin{matrix}2-x=4x-2\\2-x=2-4x\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=0\end{matrix}\right.\)

Vậy ..........