$$ \begin{aligned} 7 \cdot \frac{2x+5}{3}-3\frac{5x-7}{4} &= 10-6x&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot7 \cdot \frac{2x+5}{3}-12\cdot3\frac{5x-7}{4} &= 12\cdot10-12\cdot6x&& \text{cancel out the denominators} \\[1 em]56x+140-(45x-63) &= 120-72x&& \text{simplify left and right hand side} \\[1 em]56x+140-45x+63 &= -72x+120&& \\[1 em]11x+203 &= -72x+120&& \text{move the $ \color{blue}{ -72x } $ to the left side and $ \color{blue}{ 203 }$ to the right} \\[1 em]11x+72x &= 120-203&& \text{simplify left and right hand side} \\[1 em]83x &= -83&& \text{ divide both sides by $ 83 $ } \\[1 em]x &= -\frac{83}{83}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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