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.
To write a compound inequality that represents the range of numbers Penelope might be thinking of, we can break down the given information into two inequalities and then combine them using the "and" operator.
The given information states: "Five more than three times a number is between 23 and 32."
Let's break this down into two separate inequalities:
1. Five more than three times a number is greater than or equal to 23.
This can be represented as: 3x + 5 ≥ 23.
2. Five more than three times a number is less than or equal to 32.
This can be represented as: 3x + 5 ≤ 32.
Combining these two inequalities using the "and" operator, we get the compound inequality:
3x + 5 ≥ 23 and 3x + 5 ≤ 32
Simplifying further, we have:
23 ≤ 3x + 5 ≤ 32
Therefore, the compound inequality that shows the range of numbers Penelope might be thinking of is 23 ≤ 3x + 5 ≤ 32.
a compound inequality would mean like
a number < x < a number
you know that the number is between 23 and 32
23 < x < 32
but its not just x, its 3x +5
23 < 3x + 5 < 32