1. ## Simplifying Expressions

I have the following problem...simplify the following:

7(2 - w) - (w - 3)

This is what im getting:

= 7(2 - w) - 1(w - 3)

= 14 - 7w - w - 3

= (7 - 1)w - (14 - 3)

= 6w - 11

Apparently the answer is actually; 17 - 2w

However i don't see where i am going wrong! I think it might be something to do with a wider problem when it comes to simplifying expressions. Generally speaking i am fine when there are + operators in the equation, but the more - operators the more difficulty I have.

Can someone point me in the right direction?

Thanks.

2. Originally Posted by lee1001
I have the following problem...simplify the following:

7(2 - w) - (w - 3)

This is what im getting:

= 7(2 - w) - 1(w - 3)

= 14 - 7w - w - 3

= (7 - 1)w - (14 - 3)

= 6w - 11

Apparently the answer is actually; 17 - 2w

However i don't see where i am going wrong! I think it might be something to do with a wider problem when it comes to simplifying expressions. Generally speaking i am fine when there are + operators in the equation, but the more - operators the more difficulty I have.

Can someone point me in the right direction?

Thanks.
7(2 - w) - (w - 3)
= 7(2 - w) - 1(w - 3)
= 14 - 7w - w + 3
= (-7 - 1)w + (14 + 3)
= -8w + 17

3. Are you sure? Looking through your answer it makes sense to me but according to my maths textbook the answer to the problem:

7(2-w) - (w-3)

is...

17 - 2w

My textbook must be wrong!!

4. Originally Posted by lee1001
Are you sure? Looking through your answer it makes sense to me but according to my maths textbook the answer to the problem:

7(2-w) - (w-3)

is...

17 - 2w

My textbook must be wrong!!
I got 17 -8w, the book is wrong.

5. I checked the answer on a calculater found on QuickMath

The answer it gave is indeed 17 -8w

6. Originally Posted by lee1001
I have the following problem...simplify the following:

7(2 - w) - (w - 3)

This is what im getting:

= 7(2 - w) - 1(w - 3)

= 14 - 7w - w - 3

= (7 - 1)w - (14 - 3)

= 6w - 11

Apparently the answer is actually; 17 - 2w

However i don't see where i am going wrong! I think it might be something to do with a wider problem when it comes to simplifying expressions. Generally speaking i am fine when there are + operators in the equation, but the more - operators the more difficulty I have.

Can someone point me in the right direction?

Thanks.
$\displaystyle 7(2 - w) - (w - 3) = 7(2)+7(-w)+(-1)(w)+(-1)(-3)$
$\displaystyle 14-7w-w+3$
$\displaystyle 14-8w+3$
$\displaystyle 17-8w$