Question

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

Answer 1

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

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

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

$\Rightarrow -x>6$

Multiply both sides by $-1$, also reverse the inequality sign.

$\Rightarrow (-1)\times (-x)<(-1)\times 6$

$\Rightarrow x<-6$

Hence, $x$ is a real number which is less than $-6.$
Thus, solution set is $x\in (-\infty ,-6).$