Algebra-1

The correct option is E. {x|x∈ℝ, x ≤ -6 and x ≥ -12}.

To determine the solution set of the inequality |x + 9| - 5 ≤ -2, we can follow these steps:

Step 1: Rewrite the inequality without the absolute value:
|x + 9| - 5 ≤ -2

Step 2: Add 5 to both sides of the inequality:
|x + 9| ≤ 3

Step 3: Consider two cases:

Case 1: x + 9 is positive or zero (|x + 9| = x + 9)
In this case, we have:
x + 9 ≤ 3

Solving for x:
x ≤ 3 - 9
x ≤ -6

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

Case 2: x + 9 is negative (|x + 9| = -(x + 9) = -x - 9)
In this case, we have:
-x - 9 ≤ 3

Solving for x:
-x ≤ 3 + 9
-x ≤ 12

When we multiply both sides of the inequality by -1, the inequality sign reverses:
x ≥ -12

So, x ≥ -12 is a solution for this case.

Combining both cases, we have the solution set: {x|x∈ℝ, x ≤ -6 and x ≥ -12}. This means that x can be any real number less than or equal to -6 and any real number greater than or equal to -12.

Now let's ...