Question

Solve x3 ≥ 12. (1 point)

x3 ≥ [ ]

Answer 1

wrong

Answer 2

To solve the inequality x^3 ≥ 12, we need to isolate x.

First, we subtract 12 from both sides:
x^3 - 12 ≥ 0

Next, we can factor the left side as a difference of cubes:
(x - 2)(x^2 + 2x + 6) ≥ 0

Now, we have two cases to consider:
Case 1: (x - 2) ≥ 0 and (x^2 + 2x + 6) ≥ 0
For (x - 2) ≥ 0, x ≥ 2
For (x^2 + 2x + 6) ≥ 0, since the quadratic is always positive, there are no solutions for this case.

Case 2: (x - 2) ≤ 0 and (x^2 + 2x + 6) ≤ 0
For (x - 2) ≤ 0, x ≤ 2
For (x^2 + 2x + 6) ≤ 0, there are also no solutions, as the quadratic is always positive.

Therefore, the only solution to the inequality x^3 ≥ 12 is x ≥ 2.

Answer 3

Apologies for the mistake.

To solve the inequality x^3 ≥ 12, we need to isolate x.

First, we can cube root both sides of the inequality:
∛(x^3) ≥ ∛12

This simplifies to:
x ≥ ∛12

Since the cube root of 12 is approximately 2.289, we can say that x ≥ 2.289.