$$\frac{2x-1}{x+4} = \frac{3}{2}$$

$$ \begin{aligned} \frac{2x-1}{x+4} &= \frac{3}{2}&& \text{multiply ALL terms by } \color{blue}{ (x+4)\cdot2 }. \\[1 em](x+4)\cdot2 \cdot \frac{2x-1}{x+4} &= (x+4)\cdot2\cdot\frac{3}{2}&& \text{cancel out the denominators} \\[1 em]4x-2 &= 3x+12&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]4x-3x &= 12+2&& \text{simplify left and right hand side} \\[1 em]x &= 14&& \\[1 em]x &= 14&& \\[1 em] \end{aligned} $$

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