2x²>=-4x

To solve the inequality 2x² >= -4x, we need to manipulate the equation to isolate the variable x.

Step 1: Move all terms to one side of the inequality:

2x² + 4x >= 0

Step 2: Factor out common terms if possible. In this case, we can factor x:

x(2x + 4) >= 0

Step 3: Set each factor equal to zero and solve for x:

x = 0 (the first factor)

2x + 4 = 0 2x = -4 x = -2 (the second factor)

Step 4: Plot the points x = 0 and x = -2 on a number line:

-2 0

Step 5: Determine the sign of the inequality for different intervals on the number line. Test a point within each interval:

For x < -2, let's take x = -3: (-3)(2(-3) + 4) = (-3)(-2) = 6 > 0. The inequality is true for this interval.

For -2 < x < 0, let's take x = -1: (-1)(2(-1) + 4) = (-1)(2) = -2 < 0. The inequality is false for this interval.

For x > 0, let's take x = 1: (1)(2(1) + 4) = (1)(6) = 6 > 0. The inequality is true for this interval.

Step 6: Determine the solution:

From the analysis above, the inequality 2x² >= -4x is true for x < -2 and x > 0. Therefore, the solution can be expressed as:

x < -2 or x > 0.