Answer: We can solve the given inequality as follows:
|2x + 2| > 4
There are two cases to consider, depending on whether the expression inside the absolute value is positive or negative:
Case 1: 2x + 2 > 4
2x > 2
x > 1
Case 2: 2x + 2 < -4
2x < -6
x < -3
Therefore, the solution to the inequality is x < -3 or x > 1.
To graph the solution, we can plot the two critical points x = -3 and x = 1 on a number line, and shade the regions to the left of -3 and to the right of 1. This gives us the following graph:
<==================o-----------------o===================>
x < -3 x > 1
The open circles indicate that the points -3 and 1 are not included in the solution, since the inequality is strict (|2x + 2| > 4).
Explanation: