$$ \begin{aligned} \frac{3}{2}(4x-1)-3x &= \frac{5}{4}-(x+2)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{2}(4x-1)-4\cdot3x &= 4\cdot\frac{5}{4}-4(x+2)&& \text{cancel out the denominators} \\[1 em]24x-6-12x &= 5-(4x+8)&& \text{simplify left and right hand side} \\[1 em]12x-6 &= 5-4x-8&& \\[1 em]12x-6 &= -4x-3&& \text{move the $ \color{blue}{ -4x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]12x+4x &= -3+6&& \text{simplify left and right hand side} \\[1 em]16x &= 3&& \text{ divide both sides by $ 16 $ } \\[1 em]x &= \frac{3}{16}&& \\[1 em] \end{aligned} $$

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