$$ \begin{aligned} \frac{5}{7}(w-4)-\frac{3}{17} &= -5&& \text{multiply ALL terms by } \color{blue}{ 119 }. \\[1 em]119 \cdot \frac{5}{7}(w-4)-119\cdot\frac{3}{17} &= 119\cdot(-5)&& \text{cancel out the denominators} \\[1 em]85w-340-21 &= -595&& \text{simplify left side} \\[1 em]85w-361 &= -595&& \text{ move -361 to the right } \\[1 em]85w &= -595+361&& \\[1 em]85w &= -234&& \text{ divide both sides by $ 85 $ } \\[1 em]w &= -\frac{234}{85}&& \\[1 em] \end{aligned} $$

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