Final answer:
The inequality to determine how much money Brian could initially have is B + $11 > 5B - $11. Solving this inequality shows that Brian must start with less than $5.50 in order to have more money than Ian after Ian gives him $11.
Step-by-step explanation:
To determine how much money Brian could initially have, we can use an inequality. Let's denote Brian's initial amount of money as B. Since Ian starts with 5 times as much money as Brian, Ian's initial amount is 5B. If Ian gives $11 to Brian, then Brian's new amount becomes B + $11, and Ian's new amount becomes 5B - $11. To find out the range for Brian's initial money where he will end up with more money than Ian after the transaction, our inequality will be based on Brian having more money than Ian after receiving the $11:
B + $11 > 5B - $11
Solving this inequality involves moving all terms involving B to one side and constants to the other:
B - 5B > - $11 - $11
-4B > -$22
When we divide both sides by -4, we need to reverse the direction of the inequality (since dividing or multiplying by a negative number in an inequality reverses the inequality direction):
B < $5.50
Therefore, for Brian to have more money than Ian after Ian gives $11 to Brian, Brian must start with less than $5.50.