How Do You Solve Equations with Parentheses and Negative Signs?

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To solve the equation 8x - (3x + 2) = 2x - 10, it's essential to distribute the negative sign correctly. The expression can be rewritten as 8x - 3x - 2 = 2x - 10. After combining like terms, the equation simplifies to 3x = -12. Dividing both sides by 3 gives the solution x = -4. Proper distribution and attention to signs are crucial in solving equations with parentheses and negative signs.
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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?
 
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8x - (3x + 2) = 8x + (-1)*(3x+2)

Does that help?
 
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 alot! I forgot I could multiply by 1 so the exercise didn't change

EDIT: SOLVED!
 
Last edited:
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 :)
 
elflacodepr said:

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
 

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