$$ \begin{aligned} \frac{5}{3}+\frac{4}{3}x+3 &= 2&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot\frac{5}{3}+3\frac{4}{3}x+3\cdot3 &= 3\cdot2&& \text{cancel out the denominators} \\[1 em]5+4x+9 &= 6&& \text{simplify left side} \\[1 em]4x+14 &= 6&& \text{ move 14 to the right } \\[1 em]4x &= 6-14&& \\[1 em]4x &= -8&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{8}{4}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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