9
advanced-math

Solve: x(x+4)0x(x + 4) \geq 0

A

x0x \geq 0 or x4x \leq -4

B

4x0-4 \leq x \leq 0

C

x0x \geq 0

D

x4x \leq -4

Correct Answer: A

Choice A is the correct answer.

  1. Roots: x=0x = 0 and x=4x = -4.
  2. Region: Since it opens upward and we want 0\geq 0, we look for the outside tails.
  3. Order: 4-4 is less than 00.
  4. Solution: Left of smaller root (x4x \leq -4) or right of larger root (x0x \geq 0).

Choice B is incorrect because that is where it is negative. Choice C is incorrect because it misses the left part. Choice D is incorrect because it misses the right part.