Final answer:
The solution set for the inequality x² > 4 is all real numbers greater than 2 and less than -2, which excludes the interval [-2, 2].
Step-by-step explanation:
The given inequality is x² > 4. To find the solution set, we can start by taking the square root on both sides, keeping in mind that we need both the positive and negative square roots. This gives us two inequalities: x > 2 and x < -2. The solution set includes all the real numbers greater than 2 and less than -2, which excludes the interval [-2, 2] on the real number line. On a real number line, we represent this by drawing a line that extends to the left from -2 (not including -2) and to the right from 2 (not including 2), with open circles at -2 and 2 to indicate that these points are not part of the solution set.