Question

Solve the system of inequalities: $\frac{x+7}{x-8}>2,\frac{2x+1}{7x-1}>5$

• A. $(-\frac{16}{7},\frac{5}{7})$
• B. $(-\frac{7}{8},\frac{2}{7})$
• C. (2,5)
• D. No solution

Answer 1

The correct option is D No solution

$\frac{x+7}{x-8}>2,\frac{2x+1}{7x-1}>5$
Solving equation (1)
$x+7>2x-16$ and $x-8>0$ for $x>0$
$x<23$ and $x>8$
$\therefore ,x\in (8,23)$
Solving equation 2
$\frac{2x+1}{7x-1}>5$
$2x+1>35x-5$ and $7x-1>0$ for $x>0$
$x<\frac{6}{33}$ and $x>\frac{1}{7}$
$\therefore ,x\in (1/7,6/33)$
From both the solutions, there is no solution for x to satisfy both the equations.