MATH 62 Homework

Question

Gail is thinking of a number n, and she wants her sister to guess the number. Her first clue is that nine less than two times her number is between negative seven and one. Write a compound inequality that shows the range of numbers that Gail might be thinking of.

Answer 1

The typical form of a compound inequality is like this [smaller number] < [variable] < [larger number]

An example of this would be something like -3 < n < 2. What does this mean? It means that there is some number "n" that is bigger than -3 and also less than 2, or in other words "n" is between -3 and 2.

So now looking back at this problem, we will want to set up the compound inequality in the same way as my example. Only in this problem, instead of "n" going in the middle of the compound inequality like in my example, "nine less than two times her number" will go in the middle, so you will have to translate those words into a math expression.

This is not the answer but it would look something like this -3 < 9n - 5 < 2. I just wrote that so you would have a visual representation of what the form would look like. I hope that is enough of a hint for you to figure it out!

Answer 2

-7 < 2n - 9 < 1

2 < 2n < 10

1 < n < 5

(1,5) is the interval notation