$$ \begin{aligned} \frac{1}{2}x+\frac{3}{2}(x+1)-1 &= 5&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}x+2\frac{3}{2}(x+1)-2\cdot1 &= 2\cdot5&& \text{cancel out the denominators} \\[1 em]x+3x+3-2 &= 10&& \text{simplify left side} \\[1 em]4x+3-2 &= 10&& \\[1 em]4x+1 &= 10&& \text{ move 1 to the right } \\[1 em]4x &= 10-1&& \\[1 em]4x &= 9&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{9}{4}&& \\[1 em] \end{aligned} $$

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