A compound inequality describes a value that must meet a lower and an upper limit at the same time. Translate each limit separately, then put the variable between the two endpoints. Watch the endpoint wording: “greater than” leaves a boundary out, while “no more than” includes it.
Hints
- Hint 1
A strict inequality leaves its endpoint out. On a number line, values greater than a lower bound sit to its right. Which sign makes larger without including that bound?
- Hint 2
An inclusive inequality includes its endpoint. “No more than” allows the upper limit itself. Once you have a sign for each limit, how can you put both conditions into one chain?
Step-by-step
Translate the two price limits
Step 1Exclude the lower limit
No Desmos needed. The limit words give the price range directly. Greater than means itself is not allowed. A strict inequality leaves out its endpoint, so write:
- Step 2
Include the upper limit
No more than allows but nothing higher. An inclusive inequality includes its endpoint, so write:
- Step 3
Join the allowed limits
A compound inequality joins conditions that must hold at the same time. Put between the limits:
So an adult ticket costs more than $8 and at most $15. Check each endpoint separately to decide whether it counts. Choice B.