$$\frac{3x-5}{2} = 5x+3$$

$$ \begin{aligned} \frac{3x-5}{2} &= 5x+3&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{3x-5}{2} &= 2\cdot5x+2\cdot3&& \text{cancel out the denominators} \\[1 em]3x-5 &= 10x+6&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]3x-10x &= 6+5&& \text{simplify left and right hand side} \\[1 em]-7x &= 11&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{11}{7}&& \\[1 em] \end{aligned} $$

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