# Thread: 12 = 11x - 14x

1. ## 12 = 11x - 14x

Any hints on where I went wrong?

$\displaystyle 12 = 11x - 14x$
$\displaystyle 12 = -3x$
$\displaystyle 12/-3 = -3x/-3$
$\displaystyle -4 = x$

When checking the solution in the original equation, I got the false answer of:

$\displaystyle 12 = 11(-4) - 14(-4)$
$\displaystyle 12 = -44 - 56$
$\displaystyle 12 = 100$

2. Originally Posted by Euclid Alexandria
Any hints on where I went wrong?

$\displaystyle 12 = 11x - 14x$
$\displaystyle 12 = -3x$
$\displaystyle 12/-3 = -3x/-3$
$\displaystyle -4 = x$

When checking the solution in the original equation, I got the false answer of:

$\displaystyle 12 = 11(-4) - 14(-4)$
$\displaystyle 12 = -44 - 56$
$\displaystyle 12 = 100$
minus times minus is plus.

so -14(-4)=-(-56)=+56

RonL

3. Originally Posted by Euclid Alexandria
Any hints on where I went wrong?

$\displaystyle 12 = 11x - 14x$
$\displaystyle 12 = -3x$
$\displaystyle 12/-3 = -3x/-3$
$\displaystyle -4 = x$

When checking the solution in the original equation, I got the false answer of:

$\displaystyle 12 = 11(-4) - 14(-4)$
$\displaystyle 12 = -44 - 56$
$\displaystyle 12 = 100$
Also, even though the step that it came from was in error, -44 - 56 = -100.

-Dan

4. ## Ok, thanks guys.

The reason I became confused is, in simplifying equations like

$\displaystyle 12 = 11(-4) - 14(-4)$

I thought we were supposed to treat the negative sign in the middle as a subtraction sign. I thought we were to solve the two multiplication problems first, then subtract. I could swear I've seen situations that were similar enough in that vein, to confuse me about this situation. If that's the case, I need to learn to tell the difference.

Thankfully, at least the variable was correct this time, so I'm improving.

5. Originally Posted by Euclid Alexandria
The reason I became confused is, in simplifying equations like

$\displaystyle 12 = 11(-4) - 14(-4)$

I thought we were supposed to treat the negative sign in the middle as a subtraction sign. I thought we were to solve the two multiplication problems first, then subtract. I could swear I've seen situations that were similar enough in that vein, to confuse me about this situation. If that's the case, I need to learn to tell the difference.

Thankfully, at least the variable was correct this time, so I'm improving.
If your teacher will allow it, this might help:
When I was learning this my teacher always insisted that we write expressions like $\displaystyle x-y$ as $\displaystyle x+(-y)$. That way you never have to worry about whether or not you are adding or subtracting...you are ALWAYS adding.

Hope it helps!
-Dan

6. ## Thanks for the tip.

I was doing this for a while, but have been trying to wean myself off of it. I still use it for larger problems, but might continue sticking with it for a while in every case.

Btw, I finally noticed my error while resolving that equation, so disregard my previous post!

7. Originally Posted by Euclid Alexandria
I was doing this for a while, but have been trying to wean myself off of it. I still use it for larger problems, but might continue sticking with it for a while in every case.

Btw, I finally noticed my error while resolving that equation, so disregard my previous post!
I did that myself for a while. Believe it or not, I've come back to doing it again because the process makes it just SO much easier to find mistakes!

-Dan