x) \(\left|2x-5\right|=x+1\)
\(\Rightarrow\left[{}\begin{matrix}2x-5=x+1\\2x-5=-x-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x-x=1+5\\2x+x=-1+5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=6\\3x=4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=6\\x=\dfrac{4}{3}\end{matrix}\right.\)
y) \(\left|3x-2\right|-1=x\)
\(\Leftrightarrow\left|3x-2\right|=x+1\)
\(\Rightarrow\left[{}\begin{matrix}3x-2=x+1\\3x-2=-x-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x-x=1+2\\3x+x=-1+2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=3\\4x=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{4}\end{matrix}\right.\)
z) \(\left|3x-7\right|=2x+1\)
\(\Rightarrow\left[{}\begin{matrix}3x-7=2x+1\\3x-7=-2x-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}3x-2x=1+7\\3x+2x=-1+7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=8\\5x=6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=8\\x=\dfrac{6}{5}\end{matrix}\right.\)
v) \(\left|2x-1\right|+1=x\)
\(\Leftrightarrow\left|2x-1\right|=x-1\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=x-1\\2x-1=-x+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x-x=-1+1\\2x+x=1+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\3x=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)
