Penelope is playing a number game with her sister June. Penelope is thinking of a number and wants June to guess it. Five more thank three times a number is between 23 and 32. Write a compound inequality that shows the range of numbers that Penelope might be thinking of. Use x for your variable.
Alright, buckle up for some clown math! Let's break it down:
Penelope's number, let's call it x, is "Five more than three times a number." So we can write it as:
5 + 3x
And according to the question, this expression lies between 23 and 32. So we can write the compound inequality as:
23 ≤ 5 + 3x ≤ 32
Now, by deducting 5 from all sides, we can simplify it further:
18 ≤ 3x ≤ 27
And finally, divide everything by 3 to solve for x:
6 ≤ x ≤ 9
So, Penelope's number must be between 6 and 9. Now, let's hope June has the brains to figure it out! Good luck to her!
Let's break down the information given:
"Five more than three times a number" can be written as 3x + 5.
The range of numbers is between 23 and 32, which can be represented as:
23 ≤ 3x + 5 ≤ 32.
So, the compound inequality that shows the range of numbers Penelope might be thinking of is:
23 ≤ 3x + 5 ≤ 32.
To write a compound inequality that represents the range of numbers Penelope might be thinking of, we need to break down the given information.
The statement "Five more than three times a number" can be represented as "3x + 5".
The given range is "between 23 and 32". So, we need to represent that the number is greater than 23 and less than 32.
Combining the two conditions, the compound inequality can be written as:
23 < 3x + 5 < 32.
This inequality states that the value of 3x + 5 is between 23 and 32 but not including the endpoints.