a: \(\dfrac{2\left(x-3\right)}{4}-\dfrac{1}{2}=\dfrac{6x+9}{3}-2\)
=>\(\dfrac{x-3}{2}-\dfrac{1}{2}=\dfrac{3\left(2x+3\right)}{3}-2\)
=>\(\dfrac{x-4}{2}=2x+3-2=2x+1\)
=>\(2\left(2x+1\right)=x-4\)
=>4x+2=x-4
=>3x=-6
=>x=-2
b: \(\dfrac{2\left(3x+1\right)+1}{4}-5=\dfrac{2\left(3x-1\right)}{5}-\dfrac{3x+2}{10}\)
=>\(\dfrac{5\left[2\left(3x+1\right)+1\right]}{20}-\dfrac{100}{20}=\dfrac{2\cdot4\left(3x-1\right)}{20}-\dfrac{2\left(3x+2\right)}{20}\)
=>\(5\cdot\left(6x+2+1\right)-100=8\left(3x-1\right)-2\left(3x+2\right)\)
=>\(5\left(6x+3\right)-100=24x-8-6x-4\)
=>\(30x+15-100=18x-12\)
=>\(30x-85=18x-12\)
=>\(30x-18x=-12+85\)
=>\(12x=73\)
=>\(x=\dfrac{73}{12}\)
c: \(\dfrac{x}{3}+\dfrac{x-2}{4}=0,5x-2,5\)
=>\(\dfrac{4x+3\left(x-2\right)}{12}=0,5x-2,5\)
=>\(4x+3x-6=12\left(0,5x-2,5\right)\)
=>\(7x-6=6x-30\)
=>7x-6x=-30+6
=>x=-24
d: \(\dfrac{2x-4}{3}-2x=\dfrac{-6x+3}{5}+\dfrac{1}{15}\)
=>\(\dfrac{5\left(2x-4\right)}{15}-\dfrac{30x}{15}=\dfrac{3\left(-6x+3\right)}{15}+\dfrac{1}{15}\)
=>\(5\left(2x-4\right)-30x=3\left(-6x+3\right)+1\)
=>\(10x-20-30x=-18x+9+1\)
=>-20x-20=-18x+10
=>-2x=30
=>\(x=\dfrac{30}{-2}=-15\)
