$$ \begin{aligned} 4x+\frac{2}{8} &= 2x-\frac{7}{7}&& \text{multiply ALL terms by } \color{blue}{ 56 }. \\[1 em]56\cdot4x+56\cdot\frac{2}{8} &= 56\cdot2x-56\cdot\frac{7}{7}&& \text{cancel out the denominators} \\[1 em]224x+14 &= 112x-56&& \text{move the $ \color{blue}{ 112x } $ to the left side and $ \color{blue}{ 14 }$ to the right} \\[1 em]224x-112x &= -56-14&& \text{simplify left and right hand side} \\[1 em]112x &= -70&& \text{ divide both sides by $ 112 $ } \\[1 em]x &= -\frac{70}{112}&& \\[1 em]x &= -\frac{5}{8}&& \\[1 em] \end{aligned} $$

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