Quandaries
and Queries 

this a question for an 8th grade math student: the question is to solve and check equations and the question is 2n + 3n + 7 = 41 

Hi, I think that it helps to think of an equation as a balance like you might find in a chemistry lab. The balance has a pan on two sides and a balance point in the middle. An equatiion has numbers and symbols on the two sides and the balance point is the equal sign.(You have to stretch the analogy here a little to allow for negative weights.) In your example you have 2n + 3n + 7 on one side and 41 on the other. The object is to manipulate the weights (numbers and letters), all the time not disturbing the balance, and end with the letter n alone on one side and a number on the other side. That is you want to end with
Ther are two operations that don't disturb the balance. You can add equal weights to both sides (remember weights can be positive or negative) or you can multiply both sides by the same number. Start with
I want to end with only n on the left side so I need to eliminate the 7. I can do this by adding 7 to each side
which simplifies to
You now have five n's on the left and you want one n so multiply both sides by ^{1}/_{5}
or
Now go back to the original equation, 2n + 3n + 7 = 41, substitute the value of n you just found into the left side and verify that you get 41. Penny 

