In answering this question, I have different solutions. You can think I am crazy but this solution will lead you to the same answer if you do it right.
First, make an equation out of the given question.
Four times a number, increased by 17
4x + 17
is equal to:
9 less than six times the number:
6x - 9
What I am talking about is the technique of TRANSPOSING!!!
Transpose the numbers by transferring all the numbers from their side to one side. The numbers that are transferred SHOULD CHANGE THEIR SIGNS!!!
4x + 17 = 6x - 9
4x + 17 - 6x + 9 = 0
You can see that 6x and -9 have become -6x and +9 for they changed their signs as a result of transposing.
4x +17 - 6x + 9 = 0
After that, REDUCE!!! or you can rearrange them so that you can understand further on how it was done.
4x+17-6x+9=0 is the same with 4x+ -6x + 17 + 9 = 0
( Oh, I can subtract 4x and -6x!!! Let's do it!)
4x + -6x is the same with 4x-6x
-2x + 26 = 0
Transpose it again.
-2x = -26
4x + 17 = 6x-9
4(13) + 17 = 6(13) - 9
52 + 17 = 78-9
69 = 69
Therefore x=13 is correct.