Expert: Wei Chong - 6/23/2008

Question
My son is taking a summer course in math. It has been awhile since I was in school and I am having trouble remembering how to do muti step equations.
Such as...
3c-6(2c-3)=33-10c
If you could please respond in simple terms that would be great! Any help that you offer is greatly appreciated.
Thank You,
Amy

Answer
Hi Amy,

I'll be glad to help. Below are 3 links to resources which explain the basics behind solving multi step equations. I recommend you to watch the math videos in these links first before attempting to solve the question (scroll down to see the videos):

Removing brackets:
http://www.mathexpression.com/simplifying-algebraic-expressions.html

The basic ideas behind solving linear equations (same as solving multi step equation):
http://www.mathexpression.com/solving-linear-equation.html

Examples on solving linear equations:
http://www.mathexpression.com/solving-linear-equations.html

With the basics behind, let's solve your question step-by-step:

  3c-6(2c-3)=33-10c

1) Remove the brackets first.

Notice that we have, -6(2c-3)? we need to remove the brackets. This is shown below:

          -6(2c-3) = -6(2c) -6(-3)
                   = -12c +18

2) With this, the equation becomes:

  3c -12c +18 = 33-10c

3) Notice that we can simplify 3c -12c?  3c -12c gives -9c.
 
  -9c +18 = 33-10c
 
4) To solve this equation, we need to find c. So, we need to move all the terms with c into one side and all the other terms without c to the other side of the equation. Basically, this means that we are actually finding c = ??.

Here's how:

  -9c +18 = 33-10c             ->add +10c to both sides, this gives:
  -9c +10c +18 = 33 -10c +10c  ->simplify this, we have:  
  1c +18 = 33                  ->add -18 to both sides, this gives:
  1c +18 -18 = 33 -18          ->simplify this, we have:
  1c = 15                      ->1c is the same as c, so we have:
  c = 15

So we have, c = 15.

Best Regards,
Wei Chong