2x²>=-4x

To solve this inequality, you need to find the values of x that satisfy the given condition.

Start by moving all the terms to one side of the inequality:

2x² + 4x ≥ 0

Now, factor out the common factor, which is 2:

2(x² + 2x) ≥ 0

Now, we can focus on solving the quadratic equation x² + 2x = 0. This can be factored as:

x(x + 2) = 0

This equation is satisfied when either x = 0 or x + 2 = 0.

For x = 0, substitute it back into the original inequality:

2(0)² + 4(0) ≥ 0 0 ≥ 0

This condition is true.

For x + 2 = 0, when x = -2, substitute it back into the original inequality:

2(-2)² + 4(-2) ≥ 0 8 - 8 ≥ 0 0 ≥ 0

This condition is also true.

Therefore, the solution to the inequality 2x² + 4x ≥ 0 is x can be any real number, because any value of x satisfies the given condition.