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

$$ \begin{aligned} r+\frac{1}{4} &= -\frac{3}{2}+\frac{1}{2}r&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4r+4\cdot\frac{1}{4} &= -4\cdot\frac{3}{2}+4\frac{1}{2}r&& \text{cancel out the denominators} \\[1 em]4r+1 &= -6+2r&& \text{move the $ \color{blue}{ 2r } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]4r-2r &= -6-1&& \text{simplify left and right hand side} \\[1 em]2r &= -7&& \text{ divide both sides by $ 2 $ } \\[1 em]r &= -\frac{7}{2}&& \\[1 em] \end{aligned} $$

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