Solve 5x^2-10xgeq0

$$5 x ^ { 2 } - 10 x \geq 0$$

Solve for x

$$x\in (-\infty,0]\cup [2,\infty)$$

Solution Steps

Factor out x.

$$5x\left(x-2\right)\geq 0$$

For the product to be ≥0, x and x-2 have to be both ≤0 or both ≥0. Consider the case when x and x-2 are both ≤0.

$$x\leq 0 x-2\leq 0$$

The solution satisfying both inequalities is x\leq 0.

$$x\leq 0$$

Consider the case when x and x-2 are both ≥0.

$$x-2\geq 0 x\geq 0$$

The solution satisfying both inequalities is x\geq 2.

$$x\geq 2$$

The final solution is the union of the obtained solutions.

$$x\leq 0\text{; }x\geq 2$$