$$ \begin{aligned} \frac{4}{3}x+\frac{2}{3}x &= \frac{1}{3}x+5&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{4}{3}x+3\frac{2}{3}x &= 3 \cdot \frac{1}{3}x+3\cdot5&& \text{cancel out the denominators} \\[1 em]4x+2x &= x+15&& \text{simplify left side} \\[1 em]6x &= x+15&& \text{move the $ \color{blue}{ x } $ to the left side} \\[1 em]6x-x &= 15&& \text{simplify left side} \\[1 em]5x &= 15&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{15}{5}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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