Final answer:
To find Vince's range of heart rates, we can write and solve an absolute value inequality. The range of heart rates is 126 <= h <= 142.
Step-by-step explanation:
To find Vince's range of heart rates, we can write and solve an absolute value inequality. Let's consider the given information:
- Vince tries to keep his heart rate at 134 beats per minute.
- His actual heart rate can vary from this value by as much as 8 beats per minute.
We can represent his heart rate as h.
The absolute value inequality can be written as:
|h - 134| <= 8
To solve this inequality, we need to consider two cases: when h - 134 is positive and when h - 134 is negative.
Case 1: h - 134 is positive
In this case, the absolute value inequality can be written as:
h - 134 <= 8
Adding 134 to both sides of the inequality, we get:
h <= 142
Case 2: h - 134 is negative
In this case, the absolute value inequality can be written as:
-(h - 134) <= 8
Multiplying both sides of the inequality by -1, we get:
h - 134 >= -8
Adding 134 to both sides of the inequality, we get:
h >= 126
Therefore, combining both cases, Vince's range of heart rates is 126 <= h <= 142.