$$ \begin{aligned} x+\frac{1}{2}x-x-\frac{1}{4} &= -x+\frac{7}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4x+4 \cdot \frac{1}{2}x-4x-4\cdot\frac{1}{4} &= -4x+4\cdot\frac{7}{4}&& \text{cancel out the denominators} \\[1 em]4x+2x-4x-1 &= -4x+7&& \text{simplify left side} \\[1 em]4x+2x-4x-1 &= -4x+7&& \\[1 em]2x-1 &= -4x+7&& \text{move the $ \color{blue}{ -4x } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]2x+4x &= 7+1&& \text{simplify left and right hand side} \\[1 em]6x &= 8&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{8}{6}&& \\[1 em]x &= \frac{4}{3}&& \\[1 em] \end{aligned} $$

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