$$ \begin{aligned} \frac{3}{10}+\frac{3x+1}{20} &= -1&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20\cdot\frac{3}{10}+20\frac{3x+1}{20} &= 20\cdot(-1)&& \text{cancel out the denominators} \\[1 em]6+3x+1 &= -20&& \text{simplify left side} \\[1 em]3x+7 &= -20&& \text{ move 7 to the right } \\[1 em]3x &= -20-7&& \\[1 em]3x &= -27&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{27}{3}&& \\[1 em]x &= -9&& \\[1 em] \end{aligned} $$

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