Why Is My Solution 9x+-11 Incorrect for the Algebra Problem -6(x+2)+10+3(x-3)?

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Discussion Overview

The discussion revolves around the algebraic expression -6(x+2)+10+3(x-3) and the participant's claim of arriving at the solution 9x+-11. Participants are attempting to clarify the steps involved in simplifying the expression and identifying where the misunderstanding may lie.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states their solution as 9x+-11 and seeks help to understand the error.
  • Another participant provides a breakdown of the expression, showing the steps to combine like terms.
  • Multiple participants agree on the simplification process but disagree on the correctness of the initial claim that -6x + 3x equals 9x.
  • One participant asserts that -6x + 3x is actually -3x, challenging the previous calculations.
  • There is confusion expressed about the concept of adding terms in an expression versus an equation.
  • Another participant points out that the notation "+-11" is nonsensical and provides an alternative simplification leading to -3x - 21, which further adds 10 to yield -3x - 11.

Areas of Agreement / Disagreement

Participants generally disagree on the correctness of the initial solution of 9x+-11, with some asserting that the calculations leading to that result are incorrect. There is no consensus on the resolution of the misunderstanding, as different interpretations of the algebraic steps are presented.

Contextual Notes

Participants express uncertainty regarding the addition of terms and the interpretation of expressions versus equations, highlighting potential limitations in understanding algebraic operations.

Calista A
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this is a problem that i am working on -6(x+2)+10+3(x-3) in which i got the answer of 9x+-11 and apparently i am wrong, can someone help me understand this more.
 
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$-6(x+2) + 10 + 3(x-3) = -6x - 12 + 10 + 3x - 9$

now, combine like terms
 
skeeter said:
$-6(x+2) + 10 + 3(x-3) = -6x - 12 + 10 + 3x - 9$

now, combine like terms
i added -6x to 3x and got 9x so now i have 9x-12+10 - 9 is this correct?
 
Calista A said:
i added -6x to 3x and got 9x so now i have 9x-12+10 - 9 is this correct?

you can combine the numbers,

$$-12+10-9$$

as well
 
Calista A said:
i added -6x to 3x and got 9x so now i have 9x-12+10 - 9 is this correct?

-6x + 3x is not 9x, it's -3x.
 
Prove It said:
-6x + 3x is not 9x, it's -3x.
why... this is what i was stuck on, i thought you add on both sides which is why i was getting 9x
 
what “both sides” ?
what you posted is a single expression, not an equation.

The sum of two terms in an expression with opposite signs is the difference between the two terms, and keeping the sign of the greater term.
 
Calista A said:
why... this is what i was stuck on, i thought you add on both sides which is why i was getting 9x
How did you get -12 + 10 - 9 = -11 but not -6x + 3x = (-6 + 3)x = -3x? The addition of numbers works the same way!

-Dan
 
Calista A said:
this is a problem that i am working on -6(x+2)+10+3(x-3) in which i got the answer of 9x+-11 and apparently i am wrong, can someone help me understand this more.
First "+-11" is not a number and makes no sense.
-6(x+ 2)= -6x- 12
3(x- 3)= 3x- 9

Together they add to (-6+ 3)x- 12- 9= -3x- 21

Adding 10 to that: -3x- 11.
 

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