Algebra-1

The correct option is A. {x|x∈ℝ, x > -2 or x < -6}.

To determine the solution set of the inequality |x + 4| - 3 > -1, we can follow these steps:

Step 1: Rewrite the inequality without the absolute value:
|x + 4| - 3 > -1

Step 2: Add 3 to both sides of the inequality:
|x + 4| > 2

Step 3: Consider two cases:

Case 1: x + 4 is positive or zero (|x + 4| = x + 4)
In this case, we have:
x + 4 > 2

Solving for x:
x > 2 - 4
x > -2

So, x > -2 is a solution for this case.

Case 2: x + 4 is negative (|x + 4| = -(x + 4) = -x - 4)
In this case, we have:
-x - 4 > 2

Solving for x:
-x > 2 + 4
-x > 6

When we multiply both sides of the inequality by -1, the inequality sign reverses:
x < -6

So, x < -6 is a solution for this case.

Combining both cases, we have the solution set: {x|x∈ℝ, x > -2 or x < -6}. This means that x can be any real number greater than -2 or any real number less than ...