$$ \begin{aligned} 10 &= \frac{5}{2}(3x+10)&& \text{simplify right side} \\[1 em]10 &= \frac{15x+50}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot10 &= 2 \cdot \frac{15x+50}{2}&& \text{cancel out the denominators} \\[1 em]20 &= 15x+50&& \text{ swap the left and right side of the equation } \\[1 em]15x+50 &= 20&& \text{ move 50 to the right } \\[1 em]15x &= 20-50&& \\[1 em]15x &= -30&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= -\frac{30}{15}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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