$$ \begin{aligned} 6x+\frac{7}{7}-3 &= 5x-\frac{3}{8}&& \text{multiply ALL terms by } \color{blue}{ 56 }. \\[1 em]56\cdot6x+56\cdot\frac{7}{7}-56\cdot3 &= 56\cdot5x-56\cdot\frac{3}{8}&& \text{cancel out the denominators} \\[1 em]336x+56-168 &= 280x-21&& \text{simplify left side} \\[1 em]336x-112 &= 280x-21&& \text{move the $ \color{blue}{ 280x } $ to the left side and $ \color{blue}{ -112 }$ to the right} \\[1 em]336x-280x &= -21+112&& \text{simplify left and right hand side} \\[1 em]56x &= 91&& \text{ divide both sides by $ 56 $ } \\[1 em]x &= \frac{91}{56}&& \\[1 em]x &= \frac{13}{8}&& \\[1 em] \end{aligned} $$

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