Answer:
(-∞, -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!
