$$ \begin{aligned} \frac{5}{2}x+3 &= x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{5}{2}x+2\cdot3 &= 2x&& \text{cancel out the denominators} \\[1 em]5x+6 &= 2x&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]5x-2x &= -6&& \text{simplify left side} \\[1 em]3x &= -6&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{6}{3}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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