Question

Solve the following system of equations in R.

$\frac{2x+1}{7x-1}>5,\frac{x+7}{x-8}>2$

Answer 1

Consider the first inequation,

$\frac{2x+1}{7x-1}<5\frac{2x+1}{7x-1}-5>0\frac{2x+1-5(7x-1)}{7x-1}>02x+1-35x+5>0-33x+6>0-33x>-6x<\frac{6}{33},x>\frac{1}{7}...\left(i\right)$

Consider the second inequation,

$\frac{x+7}{x-8}>2\frac{x+7}{x-8}-2>0\frac{x+7-2(x-8)}{x-8}>0\frac{x+7-2x+16}{x-8}>0x>8,x<23...\left(ii\right)$

From (i) and (ii),there is no solution set of the simultaneous equations.