\(7,\dfrac{x-2}{4}-\dfrac{2x+3}{3}=\dfrac{x+6}{12}\)
\(\Leftrightarrow\dfrac{3\left(x-2\right)-4\left(2x+3\right)-x-6}{12}=0\)
\(\Leftrightarrow3x-6-8x-12-x-6=0\)
\(\Leftrightarrow-6x=24\)
\(\Leftrightarrow x=-4\)
\(8,\dfrac{x+2}{4}-\dfrac{5x}{6}=\dfrac{1-x}{3}\)
\(\Leftrightarrow\dfrac{3\left(x+2\right)-2\left(5x\right)-4\left(1-x\right)}{12}=0\)
\(\Leftrightarrow3x+6-10x-4+4x=0\)
\(\Leftrightarrow-3x=-2\)
\(\Leftrightarrow x=\dfrac{2}{3}\)
\(9,\dfrac{x-3}{2}-\dfrac{x+1}{10}=\dfrac{x-2}{5}\)
\(\Leftrightarrow\dfrac{5\left(x-3\right)-x-1-2\left(x-2\right)}{10}=0\)
\(\Leftrightarrow5x-15-x-1-2x+4=0\)
\(\Leftrightarrow2x=12\)
\(\Leftrightarrow x=6\)
\(10,\dfrac{2x-1}{3}+\dfrac{3x-2}{4}=\dfrac{4x-3}{5}\)
\(\Leftrightarrow\dfrac{20\left(2x-1\right)+15\left(3x-2\right)-12\left(4x-3\right)}{60}=0\)
\(\Leftrightarrow40x-20+45x-30-48x+36=0\)
\(\Leftrightarrow37x=14\)
\(\Leftrightarrow x=\dfrac{14}{37}\)
\(7,\dfrac{x-2}{4}-\dfrac{2x+3}{3}=\dfrac{x+6}{12}\\ \Rightarrow3.\left(x-2\right)-4.\left(2x+3\right)=x+6\\ \Rightarrow3x-6-8x-12-x-6=0\\ \Rightarrow-6x-24=0\\ \Rightarrow x=-4\)
\(8,\dfrac{x+2}{4}-\dfrac{5x}{6}=\dfrac{1-x}{3}\\ \Rightarrow3.\left(x+2\right)-5x.2=4\left(1-x\right)\\ \Rightarrow3x+6-10x-4+4x=0\\ \Rightarrow-3x+2=0\\ \Rightarrow x=\dfrac{2}{3}\)
\(9,\dfrac{x-3}{2}-\dfrac{x+1}{10}=\dfrac{x-2}{5}\\ \Rightarrow5.\left(x-3\right)-\left(x+1\right)=2.\left(x-2\right)\\ \Rightarrow5x-15-x-1-2x+4=0\\ \Rightarrow2x-12=0\\ \Rightarrow x=6\)
\(10,\dfrac{2x-1}{3}+\dfrac{3x-2}{4}=\dfrac{4x-3}{5}\\ \Rightarrow20.\left(2x-1\right)+15.\left(3x-2\right)=12.\left(4x-3\right)\\\Rightarrow40x-20+45x-30-48x+36=0\\ \Rightarrow37x-14=0\\ \Rightarrow x=\dfrac{14}{37}\)