For how many integers n is 3 < 5n-1 < 13?

Question

I got 4/5 < n < 14/5, but the answer choices only have from one to five. I am confused, please help.

 

Thank you.

Answer 1

integers are whole numbers so any fraction that does not divide to a whole number will not be included.  If you come up with 4/5 then the first integer above that would be 1.

 

3<5n-1<13

 

Looking at the problem as two separate entities we have:

3<5n-1              5n-1<13

5n>4                 5n<14

n>4/5                n<14/5

                         n<2 4/5

 

4/5<n<14/5

 

The first integer >4/5 is 1

The first integer less than 14/5 is 2

 

Thus n can only be the integers 1 or 2 because the problem states to only include integers. 

 

Answer 2

Your answer is correct.  Note that 14/5 = 2 and 4/5, so the only integers that lie between 4/5 and (2 and 4/5) are 1 and 2, so there are 2 such integers.