$$ \begin{aligned} \frac{7}{5}x+4 &= \frac{1}{5}+\frac{1}{5}x&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{7}{5}x+5\cdot4 &= 5\cdot\frac{1}{5}+5\frac{1}{5}x&& \text{cancel out the denominators} \\[1 em]7x+20 &= 1+x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 20 }$ to the right} \\[1 em]7x-x &= 1-20&& \text{simplify left and right hand side} \\[1 em]6x &= -19&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{19}{6}&& \\[1 em] \end{aligned} $$

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