$$-\frac{7}{2}(5x+3) = 10x-5$$

$$ \begin{aligned} -\frac{7}{2}(5x+3) &= 10x-5&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]-2 \cdot \frac{7}{2}(5x+3) &= 2\cdot10x-2\cdot5&& \text{cancel out the denominators} \\[1 em]-(35x+21) &= 20x-10&& \text{simplify left side} \\[1 em]-35x-21 &= 20x-10&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ -21 }$ to the right} \\[1 em]-35x-20x &= -10+21&& \text{simplify left and right hand side} \\[1 em]-55x &= 11&& \text{ divide both sides by $ -55 $ } \\[1 em]x &= -\frac{11}{55}&& \\[1 em]x &= -\frac{1}{5}&& \\[1 em] \end{aligned} $$

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