Pick all of the statistical questions.
How many gold medals does Brazil typically win at the Summer Olympics?
What is the most popular Olympic event of Brazilians?
How many times has Brazil hosted the Olympics?

(-∞, -12) ∪ (4, ∞)

Step-by-step explanation:

5-|x+4| is less than or equal to -3 is written as   5-|x+4| ≤ -3.

We must isolate |x+4| and then isolate x itself.

To get started, add |x+4| to both sides, obtaining 5 = |x+4| - 3.

Now add 3 to both sides:  8 = |x+4|.

One way to solve this is to realize that the "center" on the number line (x-axis) is located at -4, and that from this -4 we either add 8 (obtaining +4) or subtract 8 (obtaining -12).  Thus, the end points of the solution set are x = -12 and x = 4.  Check whether or not x = 0 satisfies the inequality:

5-|0+4| ≤ -3 => 5 - 4 ≤ -3.  This is FALSE.  The solution set does not include the numbers between -12 and +4.

Let's check out x = -13:  5-|-13+4| ≤ -3 => 5 - 9 ≤ -3, or -4 ≤ -3.  This is true!  So, numbers to the left of x = -13 and to the right of x = +4 are solutions.

Symbolically, the solution set is:

(-∞, -12) ∪ (4, ∞)

Check!