Hello, Mad!
Five times the smallest of three consecutive odd integers
is ten more than twice the largest. Find the integers.
Consecutive odd integers "go up by 2's".
Let .
. . . .
And there is your equation: .
You are correct. (Good spot! )
So let's redo this with the smallest number being 2x + 1 and the largest being 2x + 5:
As there is no integer solution for x the problem does not have a solution. (In fact you can figure this out just by doing an "even-odd" argument: 5 times an odd number is odd; 2 times an odd number plus 10 is even. So the two sides can't be equal.)
-Dan