Solve 3x/2xgeq0

$$\frac { 3 x } { 2 x } \geq 0$$

Evaluate (complex solution)

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{3}{2}\geq 0$$

Compare \frac{3}{2} and 0.

$$\text{true}$$

Solve for x

$$x\neq 0$$

Solution Steps

For the quotient to be ≥0, 3x and 2x have to be both ≤0 or both ≥0, and 2x cannot be zero. Consider the case when 3x\leq 0 and 2x is negative.

$$3x\leq 0 2x<0$$

The solution satisfying both inequalities is x<0.

$$x<0$$

Consider the case when 3x\geq 0 and 2x is positive.

$$3x\geq 0 2x>0$$

The solution satisfying both inequalities is x>0.

$$x>0$$

The final solution is the union of the obtained solutions.

$$x\neq 0$$