Question

. The difference between two natural

numbers is greater than 6 and less than
11. The greater of the two numbers is 14.
How many possible values for the
unknown number are there?

Answer 1

y = unknown number

3 < y < 8

Explanation:

Let x and y be the two natural numbers

x - y > 6 and x - y < 11

6 < x - y < 11

x is still positive after y amount is taken away from it. Since y is part of x, x is the greater value.

Hence, x=14:

6 < 14 - y < 11 ==> solve for y, the missing value

-8 < -y < -3 ==> subtract 14 on all sides

8 > y > 3 ==> Since each side is being divided by -1, switch the inequality

signs since the numbers are being divided by a negative number

3 < y < 8 ==> rearrange the inequality