Tìm x biết |x-1|=x-1

Bài 1:

a) \(\left|x-1\right|=x-1\)

\(\Rightarrow\left[{}\begin{matrix}x-1=x-1\\x-1=-x+1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x\in\varnothing\\2x=2\Rightarrow x=1\end{matrix}\right.\)

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

\(\Rightarrow\left[{}\begin{matrix}2x-3=3-2x\\2x-3=-3+2x\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}4x=6\\x\in\varnothing\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1,5\\x\in\varnothing\end{matrix}\right.\)

c) \(\left|2x-3\right|-x=5\)

\(\Rightarrow\)\(\left|2x-3\right|=5+x\)

\(\Rightarrow\)\(\left[{}\begin{matrix}2x-3=5+x\\2x-3=-5-x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\\3x=-2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=\dfrac{-2}{3}\end{matrix}\right.\)

Bài 2:

a) \(A=5-\left|2x-1\right|\)

Xét \(\left|2x-1\right|\ge0\)

\(\Rightarrow5-\left|2x-1\right|\le5\)

\(\Rightarrow Max_A=5\Leftrightarrow2x-1=0\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

\(B=-\left|x+5\right|-2017\)

Xét \(-\left|x+5\right|\le0\)

\(\Rightarrow-\left|x+5\right|-2017\le-2017\)

\(\Rightarrow Max_B=-2017\Leftrightarrow\left|x+5\right|=0\)

\(\Leftrightarrow x=-5\)

b) \(C=5+\left|x-3\right|\)

Xét \(\left|x-3\right|\ge0\)

\(\Rightarrow5+\left|x-3\right|\ge5\)

\(\Rightarrow Min_C=5\Leftrightarrow x-3=0\)

\(\Rightarrow x=3\)

\(D=\left|x-2016\right|+2017\)

Xét \(\left|x-2016\right|\ge0\)

\(\Rightarrow\left|x-2016\right|+2017\ge2017\)

\(\Rightarrow Min_D=2017\Leftrightarrow x-2016=0\)

\(\Rightarrow x=2016\)