Question

Solve the given inequality for real$x:\frac{ x}{3} > \frac{x}{2} +1$.

Answer 1

$\frac{ x}{3} > \frac{x}{2} +1$
$\frac{ x}{3} - \frac{x}{2} >1$
$⇒ \frac{2x-3x}{6} > 1$
$⇒ -\frac{x}{6} > 1$
$⇒ -x >6$
$⇒ x < -6$
Thus, all real numbers x, which are less than –6, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (–∞, –6).