\(2,\\ a,\Rightarrow\dfrac{3}{7}\left(\dfrac{1}{2}x+1\right)=\dfrac{5}{12}\\ \Rightarrow\dfrac{1}{2}x+1=\dfrac{35}{36}\\ \Rightarrow\dfrac{1}{2}x=\dfrac{71}{36}\Rightarrow x=\dfrac{71}{18}\\ b,\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{3}{4}\end{matrix}\right.\\ c,\Rightarrow\left|x-4\right|=\dfrac{1}{3}\Rightarrow\left[{}\begin{matrix}x-4=\dfrac{1}{3}\left(x\ge4\right)\\4-x=\dfrac{1}{3}\left(x< 4\right)\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{13}{3}\left(tm\right)\\x=\dfrac{11}{3}\left(tm\right)\end{matrix}\right.\)
\(3,\\ a,\dfrac{2}{x-1}< 0\Rightarrow x-1< 0\left(2>0;x-1\ne0\right)\\ \Rightarrow x< 1\\ b,\dfrac{-3}{x-6}>0\Rightarrow x-6< 0\left(-3< 0;x-6\ne0\right)\\ \Rightarrow x< 6\)
Bài 2:
a) \(\Rightarrow\dfrac{2}{3}-\dfrac{3}{14}x-\dfrac{3}{7}=\dfrac{1}{4}\)
\(\Rightarrow-\dfrac{3}{14}x=\dfrac{1}{84}\Rightarrow x=-\dfrac{1}{18}\)
b) \(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{3}{4}\end{matrix}\right.\)
c) \(\Rightarrow\left|x-4\right|=3\)
\(\Rightarrow\left[{}\begin{matrix}x-4=3\\x-4=-3\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=7\\x=1\end{matrix}\right.\)
Bài 3:
a) \(\dfrac{2}{x-1}< 0\Rightarrow x-1< 0\Rightarrow x< 1\)
b) \(-\dfrac{3}{x-6}>0\Rightarrow x-6< 0\Rightarrow x< 6\)
