$$ \begin{aligned} \frac{4}{3}x+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{4}{3}x+3\cdot1 &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]4x+3 &= 0&& \text{ move the constants to the right } \\[1 em]4x &= -3&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= -\frac{3}{4}&& \\[1 em] \end{aligned} $$

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