$$\frac{x}{3}+1 = \frac{7}{15}$$

$$ \begin{aligned} \frac{x}{3}+1 &= \frac{7}{15}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{x}{3}+15\cdot1 &= 15\cdot\frac{7}{15}&& \text{cancel out the denominators} \\[1 em]5x+15 &= 7&& \text{ move 15 to the right } \\[1 em]5x &= 7-15&& \\[1 em]5x &= -8&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{8}{5}&& \\[1 em] \end{aligned} $$

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