3 Answers

q + 23 < r + 23

q + 23 < r + 23

    - 23        - 23

------------------------------

q < r

Or,

r > q

q

q+23 < r+23

i.e q<r [subtracting 23 on both sides]

Note: This is the simple property of the inequality. So, better read and test it if you have any doubt.

q + 23 < r + 23
The idea is to get the unknowns all alone on one side of the =, <, or > sign.  In this problem, you can do that by subtracting 23 from q.  WHAT YOU DO ON ONE SIDE OF THE EQUATION, YOU MUST DO ON THE OTHER.  That means, subtract 23 from r, too.
q + 23 -23 < r + 23 - 23
NOW, you are left with just q < r.   This means that q is ANYTHING less than r.

Here's another example, just a little different, but to illustrate the "idea".
2N + 37 = 43 + N  (Get rid of the 37 by subtracting it from 2N and also by subtracting it from 43 + N (You must do the same to both sides of the equation to keep the problem balanced)

2N + 37 - 37 = 43 + N - 37
2N = 6 + N     (43 - 37 = 6)
NOW, get the Ns together.  The obvious way is to subtract the N away from 6.  IF you subtract N from 6, you must also subtract N from 2N   
2N - N = 6 + N  - N

You are left with 1N (or "N")  and 6.     N = 6   To  check your answer, substitute the "6" for N and work out the problem.

2(6) + 37 = 43 + 6
12 = 37 = 49 
49 = 49  
If you do your problems by writing down each step, soon you will understand just by looking what the final answer will be.  It's not hard, just takes a little practice and concentration.  :D