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. Show your work and write the inequality.
x + 235 > 540
_
What inequality represents all possible values of x?

What inequality represents all possible values of x?
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Answer 1

To find the inequality that represents all possible values of \( x \) (the number of miles Bradley still needs to run), we start with his goal of running at least 540 miles this month.

He's already run 235 miles, so we can express this situation with the following inequality:

\[
x + 235 \geq 540
\]

In this inequality:
- \( x \) is the number of miles he still needs to run.
- 235 miles is the total he has already run.
- 540 miles is the goal he wants to reach.

Next, we can solve the inequality for \( x \):

1. **Subtract 235 from both sides:**

\[
x \geq 540 - 235
\]

2. **Calculate \( 540 - 235 \):**

\[
540 - 235 = 305
\]

Thus, the inequality can be rewritten as:

\[
x \geq 305
\]

Now we have the inequality that represents all possible values of \( x \):

**Final Answer:**

\[
x \geq 305
\]

This means Bradley needs to run at least 305 more miles to meet his goal of 540 miles for the month.