$$ \begin{aligned} \frac{1}{8}x+17-\frac{1}{5} &= 19&& \text{multiply ALL terms by } \color{blue}{ 40 }. \\[1 em]40 \cdot \frac{1}{8}x+40\cdot17-40\cdot\frac{1}{5} &= 40\cdot19&& \text{cancel out the denominators} \\[1 em]5x+680-8 &= 760&& \text{simplify left side} \\[1 em]5x+672 &= 760&& \text{ move 672 to the right } \\[1 em]5x &= 760-672&& \\[1 em]5x &= 88&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{88}{5}&& \\[1 em] \end{aligned} $$

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