Question 242798
Define your terms:
x = number of game bank rentals
f = cost of fun guys game rentals = $10 + $3.50 * x = 10 + 3.5x.
g = cost of game bank rentals = $22 + $2.50 * x = 22 + 2.5x.
The question actually asks 2 questions
1) What value of x makes the costs the same?  
2) What is the cost?
Answering questions:
To test the value of x that makes the costs equal, set the equations equal to one another.
10 + 3.5x = 22 + 2.5x
Subtracting 2.5x from both sides.
10 + 1x = 22.  (Note that 1x is typically shown as just 'x'.)
Subtracting 10 from both sides.
x = 22 - 10 = 12.
Check your work by substituting in for values you don't know.
f = 10 + 3.5(12) = 10 + 42 = 52
g = 22 + 2.5(12) = 22 + 30 = 52
That shows the value x = 12 solves both.
And checking the solutions reveals the answer to the second question:  $52.
An interesting third question is:  Which is the better value?
Since the annual dues are paid just once, after you rent at least 12 games per year, the game bank is cheaper per rental:  $2.50 vs. the $3.50 charged by the fun guys.
So, IF you plan to rent at least 12 games per year (or 1 per month), then the game bank is less costly.