a: \(\dfrac{3x+2}{3}-\dfrac{3x+1}{6}=\dfrac{5}{3}+2x\)
=>\(\dfrac{2\left(3x+2\right)-3x-1}{6}=\dfrac{10+12x}{6}\)
=>\(2\left(3x+2\right)-3x-1=12x+10\)
=>\(6x+4-3x-1=12x+10\)
=>\(3x+3=12x+10\)
=>-9x=7
=>\(x=-\dfrac{7}{9}\)
b: \(\dfrac{x+2}{3}-\dfrac{3x-1}{5}=-2\)
=>\(\dfrac{5\left(x+2\right)-3\left(3x-1\right)}{15}=-2\)
=>\(5\left(x+2\right)-3\left(3x-1\right)=-30\)
=>\(5x+10-9x+3=-30\)
=>\(-4x=-30-13=-43\)
=>\(x=\dfrac{43}{4}\)
c: \(\dfrac{x}{20}-\dfrac{x-10}{25}=-2\)
=>\(\dfrac{5x-4\left(x-10\right)}{100}=-2\)
=>\(5x-4\left(x-10\right)=-200\)
=>\(5x-4x+40=-200\)
=>x+40=-200
=>x=-240
d: \(\dfrac{x+1}{11}-\dfrac{2x-5}{15}=\dfrac{3x-47}{17}-\dfrac{4x-59}{19}\)
=>\(\left(\dfrac{x+1}{11}-1\right)-\left(\dfrac{2x-5}{15}-1\right)=\left(\dfrac{3x-47}{17}+1\right)-\left(\dfrac{4x-59}{19}+1\right)\)
=>\(\dfrac{x-10}{11}-\dfrac{2x-20}{15}=\dfrac{3x-30}{17}-\dfrac{4x-40}{19}\)
=>\(\left(x-10\right)\left(\dfrac{1}{11}-\dfrac{2}{15}-\dfrac{3}{17}+\dfrac{4}{19}\right)=0\)
=>x-10=0
=>x=10
