What Are the Possible Values of the Larger Number in This Inequality Problem?

[frozonecom]

Homework Statement

The product of two numbers is less than 340. One of the numbers is 3 less than the other. What are the possible values of the larger number?

Homework Equations

The Attempt at a Solution

Hope this is right...

xy < 340
then, because y=x-3
x(x-3) < 340
x^2 -3x -340 < 0
(x+17)(x-20) < 0

Then, by using test numbers I got the interval (-17 , 20) as my solution set.

Now, to get the larger number, do I just add 3 to every number in my possible values for y?
Since, x=y+3 ?

Then, possible values for x (larger number) will be (-15, 23) ?
Or, is what I'm doing wrong
Edit:Okay, by simple checking, 20 x 23 is larger than 340. So I guess I can't just add 3 to every y value I have. So, how do I do it? :)
Edit:I just realized again. Since my inequality is expressed in x (larger number) doesn't that mean I got the solution set for the larger number(which is asked by problem) already?? Please correct me if I'm wrong.
EDIT 3:So sorry for the much edits, but. In order to get the y value (I'm now asking for the smaller number), do I just minus 3 to every element in my solution set, since y is defined to be x-3 ? So, solution set for y= (-20, 17)?? Again, please correct me if I'm wrong.
/HELP!

 

[CAF123]

Yes, you are correct. Another way to find the 'smallest' numbers is to express x=y+3 and solve y(y+3)<340 to find the solution set.