Edward C. answered • 03/19/15

Caltech Grad for math tutoring: Algebra through Calculus

The key thing to remember about equations is that they are like a scale that is balanced, and so any time you do something to one side of the equation you must do exactly the same thing to the other side to keep the equation balanced. The objective in solving an equation is to isolate the variable, that is you want to end up in the form

x = something

With that goal in mind, think about what you have to do to 3x+6 to end up with just x. The first thing you have to do is subtract 6. But if you subtract 6 from one side of the equation then you must also subtract 6 from the other side to keep the equation balanced. So the first step is to subtract 6 from both sides of the equation, which will leave you with

3x = 0

Now to get just x on the left hand side you must divide 3x by 3. To keep the equation balanced you must also divide 0 by 3. So the next step is to divide both sides of the equation by 3, which will leave you with

x = 0

Now you are done because you have solved the equation for x. The last step is to check the answer by plugging the answer back into the original equation to make sure it works.

Check: 3*0 + 6 = 0 + 6 = 6

It seems like a lot of work because I had to write down so much to explain it, but once you get used to doing it you'll find that you can do most of the steps in your head and all you'll need to write down is

3x + 6 = 6

3x = 0

x = 0