Penelope is playing a number game with her sister June. Penelope is thinking of a number and wants June to guess it. Five more than two times a number is between 1717 and 2121. Write a compound inequality that shows the range of numbers that Penelope might be thinking of. Use xx for your variable.
To determine the compound inequality, let's break down the given information:
The phrase "Five more than two times a number" can be represented as 2x + 5.
The inequality statement "between 1717 and 2121" can be expressed as 1717 ≤ 2x + 5 ≤ 2121.
Therefore, the compound inequality that shows the range of numbers Penelope might be thinking of would be: 1717 ≤ 2x + 5 ≤ 2121.
To write a compound inequality representing the range of numbers Penelope might be thinking of, we can use the given information: "Five more than two times a number is between 1717 and 2121."
Let's break down the information sentence by sentence:
1. "Five more than two times a number" can be written as 2x + 5, where x represents the number Penelope is thinking of.
2. "Is between 1717 and 2121" implies that the value should be greater than or equal to 1717 and less than or equal to 2121.
Putting it all together, we can write the compound inequality as follows:
1717 ≤ 2x + 5 ≤ 2121
This compound inequality represents the range of numbers that Penelope might be thinking of.
1717 <= 5+2x <= 2121
1712 <= 2x <= 2116
856 <= x <= 1058