Question

Solve the inequality for real $x$.

$x+\frac{x}{2}+\frac{x}{3}<11$

Answer 1

Given, $x+\frac{x}{2}+\frac{x}{3}<11$
$\Rightarrow x(1+\frac{1}{2}+\frac{1}{3})<11$
$\Rightarrow x\left(\frac{6+3+2}{6}\right)<11$
$\Rightarrow \frac{11x}{6}<11$
$\Rightarrow x<6$

$\Rightarrow x\in (-\infty ,6)$