How to solve for k ((−9k−7l)/4)=((−2k−5m)/7)

That’s exactly right, and that’s the only way of showing it. Well done :)

Step 1: Clear the denominators by multiplying each side by the LCM
Step 2: Distribute the coefficients to remove parentheses
Step 3: Collect like terms
Step 4: Isolate k on the left-hand side of the equation
Step 5: Solve for k

@inthenighttol You are correct in saying that is one way to represent k.

@genkan That is certainly not the only way of showing it. Mathematical expressions can usually be expressed multiple ways. Other ways to write this one include:
-((49l-20m)/55) <~ That’s what I got when I solved this problem, and it’s just as simplified as the other way of writing it.
(55/(20m-49l))^(-1) <~ This is clearly not as simple, but it is another way to write the expression.
I’m not going to list all of the possibilities because there are infinitely many, but you get the point.