+70 Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2 and the largest odd number less than 3x+5 can be written in the form ax+b . What is a+b?
We are given a positive even integer, x. The smallest odd number greater than 7x-2 can be expressed as (7x-2) + 1 = 7x - 1. The largest odd number less than 3x+5 can be expressed as (3x+5) - 1 = 3x + 4.
The positive difference between these two numbers is (7x - 1) - (3x + 4) = 7x - 3x - 1 - 4 = 4x - 5.
Now we have the difference in the form ax + b, where a = 4 and b = -5.
To find a+b, we simply add the values of a and b: a + b = 4 + (-5) = -1.
Therefore, a+b is equal to -1.
+118680 Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2 and the largest odd number less than 3x+5 can be written in the form ax+b . What is a+b?
x is even so any muliple of x is also even so
7x-2 is even and 3x+5 is odd
The smallest odd number greater than 7x-2 is 7x-1
The largest odd number less than 3x+5 is 3x+3
(7x-1)-(3x+3)
=7x-1-3x-3
=4x - 4
4+ -4 = 0
