2x²>=-4x

To solve this inequality, start by subtracting -4x from both sides: 2x² + 4x >= 0

Now, factor out a 2x from the left side of the inequality: 2x(x + 2) >= 0

We have two cases to consider:

Case 1: 2x > 0 In this case, we can divide both sides of the inequality by 2x: x + 2 >= 0 From this, we realize that x >= -2.

Case 2: 2x < 0 In this case, we divide both sides by 2: x(x + 2) <= 0 From this, we realize that x(x + 2) = 0 for x = 0 or x = -2.

To summarize the solutions, we have: x >= -2 or x = 0

So the solution to the inequality is x >= -2.