Solve the inequality x 3 >x 2 +1 for real x. - Vidyadip

Question

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

✓

Answer

Here $\frac{x}{3} > \frac{x}{2} + 1$
$ \Rightarrow \frac{x}{3} - \frac{x}{2} > 1$
$ \Rightarrow \frac{{2x - 3x}}{6} > 1$
$ \Rightarrow \frac{{ - x}}{6} > 1$
Multiplying both sides by 6, we have
-x > 6
Dividing both sides by -1, we have x < -6
Thus the solution set is $( - \infty , - 6)$

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