What is the solution set for the inequality 5-|x+4| is less than or equal to -3

(-∞, -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!  

no this is a nonlinear negative