Solve x^2<3x

$$x ^ { 2 } < 3 x$$

Solve for x

$$x\in \left(0,3\right)$$

Solution Steps

Subtract 3x from both sides.

$$x^{2}-3x<0$$

Factor out x.

$$x\left(x-3\right)<0$$

For the product to be negative, x and x-3 have to be of the opposite signs. Consider the case when x is positive and x-3 is negative.

$$x>0 x-3<0$$

The solution satisfying both inequalities is x\in \left(0,3\right).

$$x\in \left(0,3\right)$$

Consider the case when x-3 is positive and x is negative.

$$x-3>0 x<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(0,3\right)$$