Final answer:
An absolute value inequality representing numbers that are 5 units or fewer away from – 2 on the number line is |x + 2| ≤ 5, including all numbers from – 7 to 3.
Step-by-step explanation:
To write an absolute value inequality for numbers that are 5 units or fewer away from – 2 on a number line, we need to capture all the numbers that are at a distance of no more than 5 units from – 2. This includes any number from – 7 to 3 because – 2 – 5 = – 7 and – 2 + 5 = 3. Thus, the inequality can be written as:
|x + 2| ≤ 5.
This inequality states that when you take any number x, add 2 to it, and then take the absolute value, the result must be less than or equal to 5 to satisfy the condition that it is within 5 units of – 2 on the number line.