Solve the equation ,and check the solution.

r - 3 r
= __
10 13 check:

Things are a bit cluttered. 
I'm assuming the equation should be (r-3)/10 = r/13.

Use parenthesis to indicate what is being divided. In this case all of "r-3" is over 10. 

If my assumption above holds up, then we can solve for r like so
(r-3)/10 = r/13
13(r-3) = 10r ... cross multiply
13r-39 = 10r
13r-39-13r = 10r-13r ... subtract 13r from both sides
-39 = -3r
-3r = -39
-3r/(-3) = -39/(-3) ... divide both sides by -3
r = 13

The value of r is r = 13



Check:

Replace every copy of "r" with "13" to get
(r-3)/10 = r/13
(13-3)/10 = 13/13
10/10 = 13/13
1 = 1 ... equation is true; answer has been confirmed