$$ \begin{aligned} \frac{4}{5}x-2+\frac{1}{3}x &= \frac{4}{15}x+\frac{3}{15}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{4}{5}x-15\cdot2+15\frac{1}{3}x &= 15 \cdot \frac{4}{15}x+15\cdot\frac{3}{15}&& \text{cancel out the denominators} \\[1 em]12x-30+5x &= 4x+3&& \text{simplify left side} \\[1 em]17x-30 &= 4x+3&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -30 }$ to the right} \\[1 em]17x-4x &= 3+30&& \text{simplify left and right hand side} \\[1 em]13x &= 33&& \text{ divide both sides by $ 13 $ } \\[1 em]x &= \frac{33}{13}&& \\[1 em] \end{aligned} $$

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