months he runs

UpStudy Solution:

Let's analyze the given information and the equation to understand what the variable \(x\) represents in the context of Sean's jogging routine.

The equation provided is:

\(f( x) = 0.5 + 2x\)

In this equation:

- \(f( x) \) represents the total distance Sean runs after \(x\) months.

- The term \(0.5\) represents the initial distance Sean ran on his first run, which is one-half mile.

- The term \(2x\) represents the additional distance he runs each month, with \(x\) being the number of months he has been running.

To break it down further:

- \(0.5\) miles is the distance he ran on his first day.

- He increases his run by 2 miles each month, so after \(x\) months, he would have added \(2x\) miles to his initial run.

Thus, \(x\) represents the number of months he has been running. The total distance after \(x\) months is given by the initial distance plus the increase in distance over \(x\) months.

Final Answer:

The variable \(x\) represents the number of months he runs.

Key Concepts:

1. Linear Equation: An equation that models a relationship between two variables with a constant rate of change, typically in the form \(f( x) = mx + b\).

2. Understanding Variables: Variables in equations represent quantities that can change and are often used to model real-world scenarios.

Understanding these principles will be pretty helpful in interpreting the linear equations and their variables correctly within different situations. Get better, more personalized homework help at UpStudy Homework Solver. Find step-by-step solutions to your algebra questions and get comprehensive explanations on any topic from UpStudy. Download UpStudy now for an improved learning experience!