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x+7-8x/3=17/6-5x/2
$x+7-8 \cdot \frac{x}{3}=\frac{17}{6}-5 \cdot \frac{x}{2}$
Add $5 \frac{x}{2}$ to both sides
$x+7-8 \cdot \frac{x}{3}+5 \cdot \frac{x}{2}=\frac{17}{6}-5 \cdot \frac{x}{2}+5 \cdot \frac{x}{2}$
Simplify
$\frac{5 x}{6}+7=\frac{17}{6}$
Subtract 7 from both sides
$\frac{5 x}{6}+7-7=\frac{17}{6}-7$
Simplify
$\frac{5 x}{6}=-\frac{25}{6}$
Multiply both sides by 6
$\frac{6 \cdot 5 x}{6}=6\left(-\frac{25}{6}\right)$
Simplify
$5 x=-25$
Divide both sides by 5
$\frac{5 x}{5}=\frac{-25}{5}$
Simplify
$x=-5$
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