Final answer:
The compound inequality that shows the range of numbers Isabella might be thinking of is 5 < n < 9.
Step-by-step explanation:
Isabella's clue states that six less than six times her number, 6n - 6, is between 24 and 48. To represent this as a compound inequality, we can say:
24 < 6n - 6 < 48
To solve this compound inequality, we will isolate n by adding 6 to all parts of the inequality:
24 + 6 < 6n - 6 + 6 < 48 + 6
This simplifies to:
30 < 6n < 54
Next, we will divide all parts of the inequality by 6 to solve for n:
30 ÷ 6 < 6n ÷ 6 < 54 ÷ 6
This gives us the final answer:
5 < n < 9