2x²>=-4x

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

Step 1: Move all the terms to one side of the inequality to make it easier to work with. We'll subtract -4x from both sides: 2x² + 4x ≥ 0

Step 2: Factor out the common factor from the left-hand side of the inequality. In this case, the common factor is 2x: 2x(x + 2) ≥ 0

Step 3: Analyze the signs. To determine the sign of the inequality, we need to look at the signs of each factor and the sign of the inequality symbol.

• For the factor 2x, it will be positive (≥ 0) when x > 0.
• For the factor (x + 2), it will be positive (≥ 0) when x > -2.

Step 4: Determine the intervals where the inequality is satisfied. We have three regions to consider:

• When x < -2: Both factors are negative, which means the inequality is not satisfied.
• When -2 ≤ x < 0: The factor (x + 2) is positive, but 2x is negative. Therefore, the inequality is not satisfied.
• When x ≥ 0: Both factors are positive, so the inequality is satisfied.

Step 5: Write the solution. The solution to the inequality 2x² ≥ -4x is x ≥ 0.