### Instruction: The difference when the product of 4 and a number is subtracted from 16 is greater than 10. How many positive integers satisfy the given conditions?### Response: I want to find all the positive integers that make the difference between 16 and 4 times the number greater than 10.
I can write this as an inequality: 16 - 4n > 10, where n is the positive integer I'm looking for.
To solve for n, I can add 4n to both sides and subtract 10 from both sides: 6 > 4n.
Then I can divide both sides by 4 to get: 1.5 > n.
This means that n has to be less than 1.5, but also a positive integer.
The only positive integer that satisfies this condition is 1.
So there is only one positive integer that makes the difference greater than 10.