In 1996, town m had a population of 30,500 people, and it has grown at a rate of 2% every year. in 1996, town n had 32,500 people and the population has increased by a contrast rate of 600 people each year. in what year were the populations of the two towns approximately equal?

Forget the 1996 for the moment.  Just count the number of years that go by.

30500*(1.02)^x= 32500 + 600x The easiest way to handle this is either to use a spreadsheet or graph if. I don't see an algebraic way of doing it. I'll try the graph first.

The red line is y = 32500 + 600x

Now let's try a spreadsheet.

I can't copy and past a spreadsheet's contents, but it shows that they are about equal when x = 17.
y = 32500 + 600x gives 42700 when x = 17
y = 30500*(1.02)^17 gives 42707 when x = 17 You cannot get much closer than that.

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.