Question:

<p><strong>Step 1: Solve the first inequality</strong> $\frac{2x+1}{7x-1}>5$</p><p>$\frac{2x+1}{7x-1}-5>0$</p><p>$\frac{2x+1-5(7x-1)}{7x-1}>0$</p><p>$\frac{2x+1-35x+5}{7x-1}>0$</p><p>$\frac{-33x+6}{7x-1}>0$</p><p>$\frac{33x-6}{7x-1}<0$ (multiplying by -1)</p><p>Critical points: $x=\frac{6}{33}=\frac{2}{11}$ and $x=\frac{1}{7}$</p><p>Since $\frac{1}{7}≈0.143$ and $\frac{2}{11}≈0.182$, we have $\frac{1}{7}<\frac{2}{11}$</p><p>Sign analysis shows: $\frac{1}{7}<x<\frac{2}{11}$</p><p><strong>Step 2: Solve the second inequality</strong> $\frac{x+7}{x-8}>2$</p><p>$\frac{x+7}{x-8}-2>0$</p><p>$\frac{x+7-2(x-8)}{x-8}>0$</p><p>$\frac{x+7-2x+16}{x-8}>0$</p><p>$\frac{-x+23}{x-8}>0$</p><p>Critical points: $x=23$ and $x=8$</p><p>Sign analysis shows: $8<x<23$</p><p><strong>Step 3: Find intersection</strong></p><p>First inequality: $\frac{1}{7}<x<\frac{2}{11}$ (approximately $0.143<x<0.182$)</p><p>Second inequality: $8<x<23$</p><p>These intervals do not overlap, so the solution set is $\emptyset$ (empty set) or no solution.</p><p>∴ Answer: D</p>