Let the consecutive odd integers be x,x+2,x+4,andx+6
Even numbers are added to x because of the assumption that x is an odd integer and we need to add 2 to get the next odd integer. for example, if x=3, then we need to add 2 to 3 to get the next odd integer which is 5 and so on. Adding 1 will make the next number even.
Now, make and equation to match the condition given in the question,
x+(x+4) = 12{(x+2)+(x+6)}+7
or, 2x+4 = 12(2x+8)+7
or, 2x+4 =(x+4)+7
On the right side when 12 is multiplied to 2x, both the twos get cancelled and only x remains. Similarly, 4 remains after 12 is multiplied to 8.
So, now the equation becomes:
2x+4 = x+11 (Note: 4+7 = 11)
Solving for x,
2x−x = 11=4
or, x = 7
Therefore, other consecutive odd numbers are:
x+2 = 7+2=9
x+4 = 7+4=11
and,
x+6 = 7+6=13
