How do you solve linear equations by showing your work instead of just solving it from the equation???

Question

My teacher says I need to do:    _______=_____

                                             -                -

                                             ___         =___

But I just move the numbers around in the equation. Which way do you recommend and if it is my teacher's way, how do I do that??

Answer 1

Hello Buffalo Grove, IL...Itasca, IL here.

 

Well, you said that you "just move the numbers around."  Let's think about what that means with an example.  Suppose we have the following equation:

 

5x + 3 = 13

 

Let's say that you'd like to "move" the 3 from the left side to the right side.  What does the equation look like after you've "moved" the 3?

 

It might be:

 

5x = 13 + 3, and 13 + 3 is 16, so 5x = 16.

 

OR, it might be:

 

5x = 13 - 3, and 13 - 3 is 10, so 5x = 10.

 

One of those is right, and the other isn't.  :)  When you "move" that a number from one side of the equation to the other, do you just take a number, like 3, and move it? 

 

Whenever you do something to an equation, you have to make sure that the thing on the left stays equal to the thing on the right.  That's what "equals" means.  So, you don't ever just move numbers around.  That's illegal.  :)  But if you do something to one side of the equation, then as long as you do the same thing to the other side, then the thing on the left stays the same as the thing on the right, and you're fine.

 

Go back to our example, where we have 5x + 3 = 13.  Ask yourself:

 

- I want to get rid of that 3 on the left side.  What do I do to a 3 to make it into zero, so I'd have 5x + 0?  That'd "get rid of" the 3.

- Whatever I do to the left side, I have to do to the right side.  So, once you figure out what you need to do to the 3, do that same thing on the right side.

 

Your teacher wants you to show that step.  What did you do to the left and right sides of the equation, and then what does the equation now look like?

 

And if you figure that out, you now know if we have 5x = 16, or 5x = 10, and you can also show what you did to the equation to "move the 3." 

 

-- Michael

Answer 2

Not sure it is clear what you do verses what you teacher wants.

Can you write done an example?  Write a sample problem/equation.

Then write down what you write down on your paper.  I am sure we could help then.

I am curious; why didn't you just ask the teacher what he/she wanted?