Solve 3n^2<28n

$$3 n ^ { 2 } < 28 n$$

Solve for n

$$n\in \left(0,\frac{28}{3}\right)$$

Solution Steps

Subtract 28n from both sides.

$$3n^{2}-28n<0$$

Factor out n.

$$n\left(3n-28\right)<0$$

For the product to be negative, n and n-\frac{28}{3} have to be of the opposite signs. Consider the case when n is positive and n-\frac{28}{3} is negative.

$$n>0 n-\frac{28}{3}<0$$

The solution satisfying both inequalities is n\in \left(0,\frac{28}{3}\right).

$$n\in \left(0,\frac{28}{3}\right)$$

Consider the case when n-\frac{28}{3} is positive and n is negative.

$$n-\frac{28}{3}>0 n<0$$

This is false for any n.

$$n\in \emptyset$$

The final solution is the union of the obtained solutions.

$$n\in \left(0,\frac{28}{3}\right)$$