$$-22x+17 = -(5-6)+16x$$

$$ \begin{aligned} -22x+17 &= -(5-6)+16x&& \text{simplify right side} \\[1 em]-22x+17 &= -(-1)+16x&& \\[1 em]-22x+17 &= 1+16x&& \\[1 em]-22x+17 &= 16x+1&& \text{move the $ \color{blue}{ 16x } $ to the left side and $ \color{blue}{ 17 }$ to the right} \\[1 em]-22x-16x &= 1-17&& \text{simplify left and right hand side} \\[1 em]-38x &= -16&& \text{ divide both sides by $ -38 $ } \\[1 em]x &= \frac{-16}{-38}&& \\[1 em]x &= \frac{8}{19}&& \\[1 em] \end{aligned} $$

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