$$ \begin{aligned} \frac{7}{4}x-\frac{1}{4}(x+3) &= \frac{4}{7}x&& \text{multiply ALL terms by } \color{blue}{ 28 }. \\[1 em]28 \cdot \frac{7}{4}x-28\frac{1}{4}(x+3) &= 28 \cdot \frac{4}{7}x&& \text{cancel out the denominators} \\[1 em]49x-(7x+21) &= 16x&& \text{simplify left side} \\[1 em]49x-7x-21 &= 16x&& \\[1 em]42x-21 &= 16x&& \text{move the $ \color{blue}{ 16x } $ to the left side and $ \color{blue}{ -21 }$ to the right} \\[1 em]42x-16x &= 21&& \text{simplify left side} \\[1 em]26x &= 21&& \text{ divide both sides by $ 26 $ } \\[1 em]x &= \frac{21}{26}&& \\[1 em] \end{aligned} $$

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