# Math Help - Equations with variables on both sides?

1. ## Equations with variables on both sides?

Our teachers gave us a packet with the first two chapters of our book b/c they are too lazy to actually teach it. It contained no instructions, only the pages with the actual problems. I figured out multi-step... but how do you do equations with variables on both sides, such as:

7 - 2n = n - 14
(4- 2r) = -2(r+5)

It would be appreciated if you could explain all types.

2. Originally Posted by Interrobang
Our teachers gave us a packet with the first two chapters of our book b/c they are too lazy to actually teach it. It contained no instructions, only the pages with the actual problems. I figured out multi-step... but how do you do equations with variables on both sides, such as:

7 - 2n = n - 14
(4- 2r) = -2(r+5)

It would be appreciated if you could explain all types.
What you would need to do is get the variable terms on one side and the remaining terms on the other side:

$7-2n=n-14\implies 21=3n$

So solving for n, we see that $\color{red}\boxed{n=7}$

Now, the other one is different...

If you pull out a common factor of -2 from the left side, we get $-2(r-2)=-2(r+5)$

The -2 cancels out and we are left with...

$r-2=r+5\implies -2=5$ which is not true.

So there is no value for r.

Does this make sense?

--Chris

3. Originally Posted by Interrobang
b/c they are too lazy to actually teach it
Whether this is true, or not, it is NOT a useful attitude. Please modify it.