2x²>=-4x

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

Step 1: Move all terms to one side of the inequality to get a quadratic expression greater than or equal to zero. 2x² + 4x >= 0

Step 2: Factor out the common factor, which is 2x. 2x(x + 2) >= 0

Step 3: Determine the critical values, which are the values that make the expression equal to zero. In this case, the critical values are x = 0 and x = -2.

Step 4: Create a number line and mark the critical values as reference points.

      -2          0

Step 5: Test the intervals between the critical values by picking test points within each interval and substitute them into the inequality to determine the sign.

For x < -2: Pick x = -3 (a test point) 2(-3)(-3 + 2) >= 0 6 >= 0 This is true, so the inequality holds for x < -2.

For -2 < x < 0: Pick x = -1 (a test point) 2(-1)(-1 + 2) >= 0 -2 >= 0 This is false, so the inequality does not hold for -2 < x < 0.

For x > 0: Pick x = 1 (a test point) 2(1)(1 + 2) >= 0 6 >= 0 This is true, so the inequality holds for x > 0.

Step 6: Determine the solution based on the signs identified in Step 5.

The solution to the inequality 2x² >= -4x is: x <= -2 or x >= 0.