Thread: Simplifying w/ Distributive Property?

1. Simplifying w/ Distributive Property?

I have this problem:
$\displaystyle 6+2[(-8)-3(2x+4)]+10x$

And the problem is just using the distributive property to simplify this expression.

Here's the steps I've worked to solve this:
$\displaystyle 6+2[(-8)-6x+12]+10x$
$\displaystyle 6+(-16)-12x+24+10x$
$\displaystyle 6+(-16)+24-12x+10x$
$\displaystyle 14-22x$

But my answer is apparently wrong. My TI-89 calculator simplifies it out to be $\displaystyle 107-2x$.

I just want to double-check the rules for simplifying.

2. Re: Simplifying w/ Distributive Property?

Originally Posted by iLiTH
I have this problem:
$\displaystyle 6+2[(-8)-3(2x+4)]+10x$

And the problem is just using the distributive property to simplify this expression.

Here's the steps I've worked to solve this:
$\displaystyle 6+2[(-8)-6x+12]+10x$
$\displaystyle 6+(-16)-12x+24+10x$
$\displaystyle 6+(-16)+24-12x+10x$
$\displaystyle 14-22x$

But my answer is apparently wrong. My TI-89 calculator simplifies it out to be $\displaystyle 107-2x$.
$\displaystyle 6+2[(-8)-3(2x+4)]+10x=6+2[(-8)-6x-12]+10x$

3. Re: Simplifying w/ Distributive Property?

Originally Posted by Plato
$\displaystyle [(-8)-6x-12]$
Thanks for your quick reply. I just wanted to know why it would be $\displaystyle -12$, because I see the $\displaystyle -3(2x+4)$ as a positive 3 times the inside terms, because the minus symbol there seems to be just subtraction.

4. Re: Simplifying w/ Distributive Property?

Originally Posted by iLiTH
Thanks for your quick reply. I just wanted to know why it would be $\displaystyle -12$, because I see the $\displaystyle -3(2x+4)$ as a positive 3 times the inside terms, because the minus symbol there seems to be just subtraction.
$\displaystyle -3(2x+4)=-(6x+12)=-6x-12$