Question

Find the greatest integer $x$ satisfying $\frac{2x+1}{3}-\frac{3x-1}{2}>1$

Answer 1

$\frac{2x+1}{3}-\frac{3x-1}{2}>1$

$\Rightarrow \frac{4x+2-9x+3}{6}>1$

$\Rightarrow -5x+5>6$

$\Rightarrow -5x>1$

$\Rightarrow x<-1/5$

$\therefore$ the greatest integer satisfying the above inequality is $-1$.