Amelia is participating in a 60-mile spin-a-thon. Her spin bike keeps track of

the simulated number of miles she travels. She plans to take a 15-minute break

within 5 miles of riding 30 miles. Amelia spins at a constant 22mph.

Write a compound inequality that models the number of miles Amelia spins before taking a break.

25<=x<=35 (where x is miles spun before taking a break)

Step-by-step explanation:

What the question is practically asking is to explain a part of the problem already given to you, just using math symbols instead of English.

Most of the information given is not important, but we do know that Amelia will take a break and that the break will be taken "within 5 miles of riding 30 miles."

The question is asking for a Compound Inequality, which are often formatted as A
So we know that the break occurs somewhere within 5 miles of 30, so we can add and subtract 5 to get 25 and 35 (which are both exactly 5 miles away from 30).

So now we have our lowest possible and highest possible distance that Amelia can spin before taking the break, so now all that's left is to plug it in to a compound inequality.

25
However, we still have one more problem: the question says "within 5 miles," which includes 25 and 35 exactly, but our equation says that X has to be less than 35 and greater than 25.

We can solve this problem by using the handy little symbol "≤", which means less than or equal to (it's like if you combined the bottom line of an = with the < symbol).

So now our problem looks like this:

25≤x≤35

You may also want to label the variable, including units in this case:

25≤x≤35 (where x is miles spun before taking a break)