Question

( LETS SEE IF YOUR SMART )

Brittany and two of her friends want to join a softball league. The league requires teams to have at least nine players, but teams cannot have more than fifteen players. In interval notation, how many more people can join Brittany's team?

Answer 1

`6\leq x\leq 12`

Explanation:

First we have to write down what it says in the question in as an expression. So we know that there is already 3 people on Britany's team (herself and the two friends), that in order to participate in the league you will need at least 9 players, and that the team can have a maximum of 15 player. So....

Let "x" be the number of people who decided to join Britany and her friends

Let "y" be the total number of people on Britanie's team, then .....

3 + x = y

Now we need to remember that in order to participate in the league you will need at least 9 players, and that the team can have a maximum of 15 player. We can write that down as......

`9\leq y\leq 15`

Now from this we know that the minimum value that x would need to take in order for Brittany's team to participate can be found by solving 3 + x = 9. The maximum value that x would need to take in order for Brittany's team to participate can be found by solving 3 + x = 15. And so we get.....

Minimum value:

3 + x = 9

x = 9 -3

x = 6

Maximum value:

3 + x = 15

x = 15 - 3

x = 12

Now we know that x will be equal to any integer between 6 and 12 so

`6\leq x\leq 12`