$$\frac{8}{3}x-5 = -3$$

$$ \begin{aligned} \frac{8}{3}x-5 &= -3&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{8}{3}x-3\cdot5 &= 3\cdot(-3)&& \text{cancel out the denominators} \\[1 em]8x-15 &= -9&& \text{ move -15 to the right } \\[1 em]8x &= -9+15&& \\[1 em]8x &= 6&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{6}{8}&& \\[1 em]x &= \frac{3}{4}&& \\[1 em] \end{aligned} $$

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