$$\frac{17}{3}x+17-\frac{2}{3}x-15 = 0$$

$$ \begin{aligned} \frac{17}{3}x+17-\frac{2}{3}x-15 &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{17}{3}x+3\cdot17-3\frac{2}{3}x-3\cdot15 &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]17x+51-2x-45 &= 0&& \text{simplify left side} \\[1 em]15x+6 &= 0&& \text{ move the constants to the right } \\[1 em]15x &= -6&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= -\frac{6}{15}&& \\[1 em]x &= -\frac{2}{5}&& \\[1 em] \end{aligned} $$

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