$$ \begin{aligned} \frac{y+7}{3} &= \frac{1}{3}y+\frac{7}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{y+7}{3} &= 3 \cdot \frac{1}{3}y+3\cdot\frac{7}{3}&& \text{cancel out the denominators} \\[1 em]y+7 &= y+7&& \text{move the $ \color{blue}{ y } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]y-y &= 7-7&& \text{simplify left and right hand side} \\[1 em]y-y &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$

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