Acharges $9.95 per month for the first 10 hours of use and $1.69 per hour for all those over 10. provider b charges a flat fee of $19.95.

Given:
A = charges 9.95 per month for the first 10 hours and 1.69 per hour for all those over 10 hours.
B = charges a flat fee of 19.95

A = 9.95 + 1.69(x-10)  where x is the total number of hours used.
B = 19.95

A = B
9.95 + 1.69(x - 10) = 19.95
1.69x - 16.9 = 19.95 - 9.95 
1.69x = 10 + 16.9
1.69x = 26.9
x = 26.9/1.69
x = 15.92 hours

If usage does not go over 10 hours, it is cheaper to use A. 
If usage is between 15-16 hours, A or B is acceptable. They cost almost the same. 
If usage is beyond 16 hours, it is cheaper to use B.

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.