How Do You Solve Equations with Parentheses and Negative Signs?

[elflacodepr]

Homework Statement

I want to solve this equation: 8x - (3x + 2) = 2x - 10


2. The attempt at a solution
I tried this:
8x - (3x + 2) = 2x - 10

(3x + 2) = 2x - 8x -10
(3x + 2) = -6x - 10

I know how to break parenthesis when there are no signs between a number and the parenthesis...but the exercise has a minus sign between 8x and (3x + 2) which separates them, how do I solve this?

 

[Feldoh]

8x - (3x + 2) = 8x + (-1)*(3x+2)

Does that help?

 

[elflacodepr]

Yes that helped! This is what I did:

8x - (3x + 2) = 2x - 10

8x - 1(3x + 2) = 1(2x - 10)

8x - 3x -2 = 2x - 10

_{(Now I move all variables together)}
8x - 3x -2x = -2 - 10

3x = -12

3x/3 = -12/3

_{(3's are canceled)}
x = -4

Thanks a lot! I forgot I could multiply by 1 so the exercise didn't change

EDIT: SOLVED!

 

[Feldoh]

That's the correct way to distribute! But watch out when going from:

8x - 3x -2 = 2x - 10

to

8x - 3x -2x = -2 - 10

The sign on your 2 needs to be fixed :)

 

[abstrakt!]

Homework Statement

I want to solve this equation: 8x - (3x + 2) = 2x - 10


2. The attempt at a solution
I tried this:
8x - (3x + 2) = 2x - 10

(3x + 2) = 2x - 8x -10
(3x + 2) = -6x - 10

I know how to break parenthesis when there are no signs between a number and the parenthesis...but the exercise has a minus sign between 8x and (3x + 2) which separates them, how do I solve this?

Alternatively:

$8x-(3x + 2)=2x -10$

$8x-3x-2=2x-10$