+0

-1
33
5

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?

Jun 12, 2023

#1
+1

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.

Jun 12, 2023
#3
+2

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

Jun 13, 2023