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------------------------------------------------ Chan is in a running club and needs to run at least 500 miles in a year to earn the gold level of achievement. He is presently at 220 miles. Which inequality can be used to determine the additional number of miles he must run to earn gold?

A. [tex]x + 220 \lt 500[/tex]

B. [tex]x + 220 \geq 500[/tex]

C. [tex]x + 500 \gt 220[/tex]

D. [tex]x + 500 \leq 220[/tex]

To help Chan earn the gold level of achievement in his running club, we need to determine the additional number of miles he can run to reach at least 500 miles in a year. He's already completed 220 miles so far.

Let's set up an inequality to solve this problem:

Chan needs to run a total of 500 miles. He's already run 220 miles. Therefore, we need to find out how many more miles, say [tex]\( x \)[/tex], he needs to run.

The expression for the additional miles is:
[tex]\[ x + 220 \][/tex]

We want this total to be at least 500 miles:
[tex]\[ x + 220 \geq 500 \][/tex]

Thus, the correct inequality that represents this situation is:
[tex]\[ x + 220 \geq 500 \][/tex]

This inequality shows that the remaining miles plus his current 220 miles should be greater than or equal to 500 miles. The correct choice from the provided options is (B) [tex]\( x + 220 \geq 500 \)[/tex].