2009 - | 2009 - x | = x
| x - 2009 | = 2009 - x
x - 2009 = 2009 + x
x + x = 2009 + 2009
x = 2009
\(2009-|2009-x|=x\)
\(\Leftrightarrow\)\(|2009-x|=2009-x\)
\(DK:2009-x\ge0\Leftrightarrow x\ge-2009\)
\(\Leftrightarrow\orbr{\begin{cases}2009-x=2009-x\\2009-x=-\left(2009-x\right)\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}-x+x=2009-2009\\2009-x=-2009+x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}0x=0\left(lọai\right)\\-x-x=-2009-2009\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}0x=0\left(loai\right)\\-2x=-4018\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}0x=0\left(loai\right)\\x=-4018:\left(-2\right)\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}0x=0\left(loai\right)\\x=2009\left(chon\right)\end{cases}}\)
Vậy x=2009
