Bài 1:
\(a,3\left(x-11\right)-2\left(x+11\right)=2011\)
\(\Leftrightarrow3x-33-2x-22=2011\)
\(\Leftrightarrow x-55=2011\)
\(\Leftrightarrow x=2066\)
Vậy pt có nghiệm x = 2066
\(b,\left(x-1\right)\left(3x-7\right)=\left(x-1\right)\left(x+30\right)\)
\(\Leftrightarrow\left(x-1\right)\left(3x-7\right)-\left(x-1\right)\left(x+30\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x-7-x-30\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(2x-37\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\2x-37=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{37}{2}\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{1;\dfrac{37}{2}\right\}\)
\(c,\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x^2-2x}\) (1)
ĐKXĐ : \(\left\{{}\begin{matrix}xe0\\xe2\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow\dfrac{x\left(x+2\right)}{x\left(x-2\right)}-\dfrac{x-2}{x\left(x-2\right)}=\dfrac{2}{x\left(x-2\right)}\)
\(\Rightarrow x^2+2x-x+2-2=0\)
\(\Leftrightarrow x^2+x=0\)
\(\Leftrightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{0;-1\right\}\)
\(d,\left|2x-3\right|=x+1\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=x+1\\2x-3=-x-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-x=1+3\\2x+x=-1+3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\3x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{2}{3}\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{4;\dfrac{2}{3}\right\}\)
Bài 2:
\(a,2\left(x-1\right)< x+1\)
\(\Leftrightarrow2x-2< x+1\)
\(\Leftrightarrow2x-x< 1+2\)
\(\Leftrightarrow x< 3\)
Vậy bpt có nghiệm x < 3
b, Đề bài ko rõ
