At a local fitness center, members pay a $10 membership fee and $5 for each aerobics class. nonmembers pay $6 for each aerobics class. for what number of aerobics classes will the cost for members and nonmembers be the same?

One way to solve it is writing two equations based on the info so

y = 5x + 10 for members
y = 6x for nonmembers

(the + 10 isn't included in the second equation because nonmembers won't pay a membership fee)

and to find their intersection point (where the values will be the same), you just set them equal to each other:

5x + 10 = 6x

subtract 5x

x = 10 classes

Distance is always positive