Solve 0<4x^2-3x

$$0 < 4 x ^ { 2 } - 3 x$$

Solve for x

$$x\in \left(-\infty,0\right)\cup \left(\frac{3}{4},\infty\right)$$

Solution Steps

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$4x^{2}-3x>0$$

Factor out x.

$$x\left(4x-3\right)>0$$

For the product to be positive, x and x-\frac{3}{4} have to be both negative or both positive. Consider the case when x and x-\frac{3}{4} are both negative.

$$x<0 x-\frac{3}{4}<0$$

The solution satisfying both inequalities is x<0.

$$x<0$$

Consider the case when x and x-\frac{3}{4} are both positive.

$$x-\frac{3}{4}>0 x>0$$

The solution satisfying both inequalities is x>\frac{3}{4}.

$$x>\frac{3}{4}$$

The final solution is the union of the obtained solutions.

$$x<0\text{; }x>\frac{3}{4}$$