Question

Solve the given inequality for real $x:x+\frac{x}{2}+\frac{x}{3}<11.$

Answer 1

Solve inequality
Given : $x+\frac{x}{2}+\frac{x}{3}<11$

$\Rightarrow \frac{6x+3x+2x}{6}<11$

$\Rightarrow 6x+3x+2x<11\times 6$

$\Rightarrow 11x<66$

$\Rightarrow x<\frac{66}{11}$

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