$$ \begin{aligned} 4x+\frac{1}{15} &= 2 \cdot \frac{x}{10}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30\cdot4x+30\cdot\frac{1}{15} &= 30\cdot2 \cdot \frac{x}{10}&& \text{cancel out the denominators} \\[1 em]120x+2 &= 6x&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]120x-6x &= -2&& \text{simplify left side} \\[1 em]114x &= -2&& \text{ divide both sides by $ 114 $ } \\[1 em]x &= -\frac{2}{114}&& \\[1 em]x &= -\frac{1}{57}&& \\[1 em] \end{aligned} $$

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