$$ \begin{aligned} \frac{1}{2}x+\frac{1}{3} &= \frac{1}{5}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{1}{2}x+30\cdot\frac{1}{3} &= 30\cdot\frac{1}{5}&& \text{cancel out the denominators} \\[1 em]15x+10 &= 6&& \text{ move 10 to the right } \\[1 em]15x &= 6-10&& \\[1 em]15x &= -4&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= -\frac{4}{15}&& \\[1 em] \end{aligned} $$

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