$$ \begin{aligned} 5(\frac{1}{2}f-\frac{1}{4}) &= 6+f&& \text{simplify left and right hand side} \\[1 em]5(\frac{f}{2}-\frac{1}{4}) &= f+6&& \\[1 em]5 \cdot \frac{2f-1}{4} &= f+6&& \\[1 em]\frac{10f-5}{4} &= f+6&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{10f-5}{4} &= 4\cdot1f+4\cdot6&& \text{cancel out the denominators} \\[1 em]10f-5 &= 4f+24&& \text{move the $ \color{blue}{ 4f } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]10f-4f &= 24+5&& \text{simplify left and right hand side} \\[1 em]6f &= 29&& \text{ divide both sides by $ 6 $ } \\[1 em]f &= \frac{29}{6}&& \\[1 em] \end{aligned} $$

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