\(\dfrac{2x+1}{5}-\dfrac{4x-2}{4}=10x\Leftrightarrow\dfrac{4\left(2x+1\right)}{20}-\dfrac{5\left(4x-2\right)}{20}=\dfrac{10x.20}{20}\)
\(\Leftrightarrow4\left(2x+1\right)-5\left(4x-2\right)=200x\)
\(\Leftrightarrow8x+4-20x+10=200x\)
\(\Leftrightarrow8x-20x-200x=-4-10\)
\(\Leftrightarrow-228x=-14\)\(\Leftrightarrow-\dfrac{14}{-228}=\dfrac{7}{114}\)
\(\dfrac{2x+1}{5}-\dfrac{4x-2}{4}=10x\)
\(\rightarrow\dfrac{8x+4}{20}-\dfrac{20x-10}{20}=10x\)
\(\rightarrow\dfrac{\left(8x+4\right)-\left(20x-10\right)}{20}=10x\)
\(\rightarrow\dfrac{8x+4-20x+10}{20}=10x\)
\(\rightarrow\dfrac{\left(8x-20x\right)+\left(4+10\right)}{20}=10x\)
\(\rightarrow\dfrac{-12x+14}{20}=10x\)
\(\rightarrow\left(-12x\right)+14=10x.20\)
\(\rightarrow\left(-12x\right)+14=200x\)
\(\rightarrow14=200x-\left(-12x\right)\)
\(\rightarrow14=200x+12x\)
\(\rightarrow14=\left(200+12\right)x\)
\(\rightarrow14=212x\)
\(\rightarrow14:212=x\)
\(\rightarrow\dfrac{14}{212}=x\)
\(\rightarrow\dfrac{7}{106}=x\)
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