How many different integer values of n satisfy the inequality 1/13 < 2/n < 1/10?
F. 1
G. 2
H. 3
J. 4
K. 5
2
To solve the inequality 1/13 < 2/n < 1/10, we need to find the range of possible values for n.
First, let's find the lower bound by solving the inequality 1/13 < 2/n:
Multiply both sides of the inequality by n to eliminate the fraction:
n*(1/13) < 2
n/13 < 2
Multiply both sides of the inequality by 13 to isolate n:
n < 2*13
n < 26
Next, let's find the upper bound by solving the inequality 2/n < 1/10:
Multiply both sides of the inequality by n to eliminate the fraction:
2 < n*(1/10)
2 < n/10
Multiply both sides of the inequality by 10 to isolate n:
20 < n
Therefore, the range of possible values for n is 20 < n < 26.
Now, let's determine how many different integer values satisfy this inequality between 20 and 26.
We can list the integers between 20 and 26: 21, 22, 23, 24, 25.
There are 5 integers between 20 and 26 that satisfy the inequality.
Therefore, the answer is option K. 5.