Answer:
[-5,-13]
Explanation:
To solve this, start by getting rid of the -1 by adding 1 to 8 now you're left with:
|x - 4| ≤ 9 now you will solve this like a regular absolute value inequality
Because the equation withing the absolute value signs can be negative, you will solve this equation twice, once with a negative answer, and the next time, with a positive answer. However, in order to get a negative answer the sign ≤ needs to be flipped. Now we can solve.
Equation 1:
x - 4 ≤ 9 add 4 to -4 so it cancels out, then add it to 9
x ≤ 13
Equation 2:
x - 4 ≥ -9 add 4 to -4 so it cancels out, then add it to -9
x ≥ -5
Both of these equations can be simplified and turned into one compound inequality:
-5 ≤ x ≤ 13
In interval notation, this would be written as:
[-5,13]