Final answer:
To solve |2x + 4| < 6, two cases are considered based on whether the expression inside the absolute value is non-negative or negative. This results in the combined interval (-5, 1), which is the correct answer.
Step-by-step explanation:
To find the solution set of the inequality |2x + 4| < 6, we first consider two cases based on the definition of absolute value.
Case 1: If the expression inside the absolute value is positive or zero, we have 2x + 4 < 6. Subtracting 4 from both sides gives 2x < 2, and dividing by 2 gives x < 1. So, for this case, the solutions are all x less than 1.
Case 2: If the expression inside the absolute value is negative, we consider -(2x + 4) < 6. Multiplying the inequality by -1 (and remembering to reverse the inequality) gives 2x + 4 > -6. Then, subtracting 4 from both sides gives 2x > -10, and dividing by 2 gives x > -5.
Thus, combining both cases, we have x > -5 and x < 1, which is represented in interval notation as (-5, 1).
The correct answer is option a) (-5, 1).