a) Vì \(2010-\left|x-2010\right|=x\)
\(\Rightarrow\left|x-2010\right|=2010-x\)
\(\Rightarrow\left|x-2010\right|=-\left(x-2010\right)\)
\(\Rightarrow x-2010\le0\)
\(\Rightarrow x\le2010\)
Vậy \(x\le2010.\)
b) \(\left|3x-4\right|+\left|3x+5\right|=9\)
\(\Rightarrow\left|4-3x\right| +\left|3x+5\right|=9\)
Nhận thấy \(\left|4-3x\right|\ge4-3x\)
\(\left|3x+5\right|\ge3x +5\)
\(\Rightarrow\left|4-3x\right|+\left|3x+5\right|\ge4-3x+3x+5\)
\(\Rightarrow\left|4-3x\right|+\left|3x+5\right|\ge9\)
Dấu \("="\) xảy ra khi:
\(\left[{}\begin{matrix}4-3x\ge0\\3x+5\ge0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}3x\le4\\3x\ge-5\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x\le\dfrac{4}{3}\\x\ge\dfrac{-5}{3}\end{matrix}\right.\)
\(\Rightarrow\dfrac{-5}{3}\le x\le\dfrac{4}{3}.\)
Vậy \(\dfrac{-5}{3}\le x\le\dfrac{4}{3}.\)
