2x²>=-4x

To solve the inequality 2x² >= -4x, we can follow these steps:

Step 1: Move all terms to one side of the inequality: 2x² + 4x >= 0

Step 2: Factor out common terms, if possible: 2x(x + 2) >= 0

Step 3: Determine the sign of each factor: For the inequality to be true, either both factors must be positive or both factors must be negative.

Case 1: x + 2 > 0 and x > 0 x + 2 > 0: Subtract 2 from both sides: x > -2 x > 0: This condition is already satisfied by this case.

Case 2: x + 2 < 0 and x < 0 x + 2 < 0: Subtract 2 from both sides: x < -2 x < 0: This condition is already satisfied by this case as well.

Step 4: Combine the cases: The common solution interval is -2 < x < 0.

Therefore, the solution to the inequality 2x² >= -4x is -2 < x < 0.