$$ \begin{aligned} 4x-\frac{8}{5} &= 3x+\frac{2}{2}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot4x-10\cdot\frac{8}{5} &= 10\cdot3x+10\cdot\frac{2}{2}&& \text{cancel out the denominators} \\[1 em]40x-16 &= 30x+10&& \text{move the $ \color{blue}{ 30x } $ to the left side and $ \color{blue}{ -16 }$ to the right} \\[1 em]40x-30x &= 10+16&& \text{simplify left and right hand side} \\[1 em]10x &= 26&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{26}{10}&& \\[1 em]x &= \frac{13}{5}&& \\[1 em] \end{aligned} $$

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