Solve 1-y/ygeq0

$$\frac{ 1-y }{ y } \geq 0$$

Solve for y

$$y\in (0,1]$$

Solution Steps

For the quotient to be ≥0, 1-y and y have to be both ≤0 or both ≥0, and y cannot be zero. Consider the case when 1-y\leq 0 and y is negative.

$$1-y\leq 0 y<0$$

This is false for any y.

$$y\in \emptyset$$

Consider the case when 1-y\geq 0 and y is positive.

$$1-y\geq 0 y>0$$

The solution satisfying both inequalities is y\in \left(0,1\right].

$$y\in (0,1]$$

The final solution is the union of the obtained solutions.

$$y\in (0,1]$$