Question

Bradley has a goal to run at least 540 miles this month. He has been running for 2 weeks and has run a total of 235
miles already. The inequality below shows x, the number of miles he will need to run in order to complete his
goal. (2 points - Show your work and write the inequality)
x + 235 ≥ 540

What inequality represents all possible values of x?

Answer 1

To find the inequality that represents all possible values of \( x \) that Bradley needs to run in order to meet his goal of at least 540 miles for the month, we start with the total miles he needs to run, which is 540 miles.

Since he has already run 235 miles, we can express the relationship with the inequality as follows:

1. Let \( x \) be the number of miles he needs to run to reach his goal.
2. The total miles run is the sum of the miles he has already run (235) and the miles he will run (x).
3. To complete his goal, this total must be at least 540:

\[
x + 235 \geq 540
\]

Now, we can solve for \( x \):

1. Subtract 235 from both sides:

\[
x \geq 540 - 235
\]

2. Calculate the right side:

\[
540 - 235 = 305
\]

Thus, the inequality that represents all possible values of \( x \) is:

\[
x \geq 305
\]

To summarize:
- The inequality is \( x + 235 \geq 540 \).
- The simplified form is \( x \geq 305 \).