Question

1, tìm x biết 2011-|x-2011|=x

Answer 1

\(2011-\left|x-2011\right|=x\)

\(\Rightarrow\left|x-2011\right|=2011-x\)

\(\Rightarrow x-2011=\pm\left(2011-x\right)\)

+) \(x-2011=2011-x\)

\(\Rightarrow2x=2011+2011\)

\(\Rightarrow x=2011\) ( chọn )

+) \(x-2011=-\left(2011-x\right)\)

\(\Rightarrow x-2011=-2011+x\)

\(\Rightarrow0=0\) ( vô lí )

Vậy \(x=2011\)

 

Answer 2

$2011 - |x-2011| = x$

$\iff |x-2011| = 2011 - x$

$\iff x -2011 \leqslant 0$

$\iff x \leqslant 2011$