$$ \begin{aligned} \frac{15}{10}x+3 &= 18-\frac{15}{10}x&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{15}{10}x+10\cdot3 &= 10\cdot18-10 \cdot \frac{15}{10}x&& \text{cancel out the denominators} \\[1 em]15x+30 &= 180-15x&& \text{move the $ \color{blue}{ -15x } $ to the left side and $ \color{blue}{ 30 }$ to the right} \\[1 em]15x+15x &= 180-30&& \text{simplify left and right hand side} \\[1 em]30x &= 150&& \text{ divide both sides by $ 30 $ } \\[1 em]x &= \frac{150}{30}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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