Solve the given inequality for real x:


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



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

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

$\Rightarrow \frac{11 x}{6}<11$

$\Rightarrow \frac{11 x}{6 \times 11}<\frac{11}{11}$

$\Rightarrow \frac{x}{6}<1$

$\Rightarrow x<6$

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 $(-\infty, 6)$.


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