Question

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

Answer 1

Consider the given inequality,

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

Multiply by $6$ on both sides, we get

$6\times \frac{x}{3}>6\times \frac{x}{2}+6\times 1$

$2x>3x+6$

$2x-3x>3x-3x+6$

$-x>6$

$x<-6$

Hence, this is the answer.