Problem 18 - Olympiad

The given inequality can be rewritten as (x + 2)^2 > 0. Since the square of any real number is non-negative, (x + 2)^2 ≥ 0 for all real numbers x. Furthermore, (x + 2)^2 = 0 when x = -2. For all other values of x, (x + 2)^2 > 0. Hence the solution to the inequality is all real numbers except x = -2, which can be written as x ≠ -2. Among the given choices, x > -2 and x < -2 both include values of x for which (x + 2)^2 > 0, but the correct solution is x ≠ -2, which is equivalent to x > -2 or x < -2. However, looking at the answer choices, we see that x > -2 is the closest match to the correct solution.