The solution set for the inequality |x + 2| > 2 is x < - 4 or x > 0. (Correct choice: C)
How to solve an inequality that involves absolute values
In this question we find the case of an inequality involving absolute values, whose solution set must be found by means of algebra properties and definition of absolute value. First, write the entire inequality:
|x + 2| > 2
Second, use the definition of absolute value to eliminate absolute value symbols:
x + 2 < - 2 or x + 2 > 2
Third, solve for the resulting cases:
x < - 4 or x > 0
Hence, the correct graph that represents inequality is option C.