Solve .5x^2geq2x

$$.5 x ^ { 2 } \geq 2 x$$

Solve for x

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

Solution Steps

Subtract 2x from both sides.

$$0.5x^{2}-2x\geq 0$$

Factor out x.

$$x\left(0.5x-2\right)\geq 0$$

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

$$x\leq 0 x-4\leq 0$$

The solution satisfying both inequalities is x\leq 0.

$$x\leq 0$$

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

$$x-4\geq 0 x\geq 0$$

The solution satisfying both inequalities is x\geq 4.

$$x\geq 4$$

The final solution is the union of the obtained solutions.

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