Solve y^2geq4y

$$y ^ { 2 } \geq 4 y$$

Solve for y

$$y\in (-\infty,0]\cup [4,\infty)$$

Solution Steps

Subtract 4y from both sides.

$$y^{2}-4y\geq 0$$

Factor out y.

$$y\left(y-4\right)\geq 0$$

For the product to be ≥0, y and y-4 have to be both ≤0 or both ≥0. Consider the case when y and y-4 are both ≤0.

$$y\leq 0 y-4\leq 0$$

The solution satisfying both inequalities is y\leq 0.

$$y\leq 0$$

Consider the case when y and y-4 are both ≥0.

$$y-4\geq 0 y\geq 0$$

The solution satisfying both inequalities is y\geq 4.

$$y\geq 4$$

The final solution is the union of the obtained solutions.

$$y\leq 0\text{; }y\geq 4$$