$$ \begin{aligned} 1-2x-\frac{4}{10} &= 2x-\frac{5}{5}+\frac{x}{15}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30\cdot1-30\cdot2x-30\cdot\frac{4}{10} &= 30\cdot2x-30\cdot\frac{5}{5}+30\frac{x}{15}&& \text{cancel out the denominators} \\[1 em]30-60x-12 &= 60x-30+2x&& \text{simplify left and right hand side} \\[1 em]-60x+18 &= 62x-30&& \text{move the $ \color{blue}{ 62x } $ to the left side and $ \color{blue}{ 18 }$ to the right} \\[1 em]-60x-62x &= -30-18&& \text{simplify left and right hand side} \\[1 em]-122x &= -48&& \text{ divide both sides by $ -122 $ } \\[1 em]x &= \frac{-48}{-122}&& \\[1 em]x &= \frac{24}{61}&& \\[1 em] \end{aligned} $$

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