How Do You Solve Equations with Parentheses and Negative Signs?

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In summary, to solve the equation 8x - (3x + 2) = 2x - 10, one can distribute the negative sign to the terms inside the parentheses, combine like terms, and solve for x by isolating the variable. Alternatively, one can move all variables to one side of the equation and use properties of equality to solve for x. The solution is x = -4.
  • #1
elflacodepr
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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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  • #2
8x - (3x + 2) = 8x + (-1)*(3x+2)

Does that help?
 
  • #3
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!
 
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  • #4
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 :)
 
  • #5
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:

[itex] 8x-(3x + 2)=2x -10[/itex]

[itex]8x-3x-2=2x-10[/itex]
 

FAQ: How Do You Solve Equations with Parentheses and Negative Signs?

How do I break parenthesis in a mathematical equation?

To break parenthesis in a mathematical equation, you can use the distributive property. This means that you can multiply the term outside the parenthesis by each term inside the parenthesis. Make sure to follow the order of operations.

Can I break parenthesis in a sentence?

Yes, you can break parenthesis in a sentence by removing the information inside the parenthesis. This can be done if the information is not essential to the meaning of the sentence. If the information is important, you can rewrite the sentence without using parenthesis.

How can I break parenthesis in a code?

In coding, parenthesis are often used for grouping and organizing code. To break parenthesis in a code, you can use the same method as breaking parenthesis in a mathematical equation. You can also use functions or methods to manipulate the code within the parenthesis.

Is it always necessary to break parenthesis?

No, it is not always necessary to break parenthesis. Parenthesis are used to group information or indicate order of operations. If the information inside the parenthesis is already clear and does not affect the overall meaning, then it is not necessary to break the parenthesis.

Are there any rules for breaking parenthesis?

Yes, there are some rules for breaking parenthesis. When breaking parenthesis in a mathematical equation, you must follow the order of operations. In a sentence, you should only break parenthesis if the information is not essential to the meaning. In coding, you must make sure that the code still runs properly after breaking the parenthesis.

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