Quick solve for X type fraction question.

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Homework Help Overview

The discussion revolves around solving a fractional equation of the form 2 = (x + 2) / (x - 6). Participants are attempting to understand the steps involved in manipulating the equation to isolate x.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the initial approach of multiplying both sides by 2 and discussing alternative methods to eliminate the fraction. There is also a focus on verifying the correctness of the proposed solution x = 14.

Discussion Status

Some participants are providing guidance on how to approach the problem, while others are expressing confusion about the correctness of the proposed solution. Multiple interpretations of the steps involved are being explored, particularly regarding the manipulation of the equation.

Contextual Notes

There is a noted discrepancy between the proposed solution and the expected outcome, with participants questioning the validity of the answer x = 14 based on the original equation. Additionally, a new problem involving a different fractional equation is introduced, indicating a broader context of inquiry.

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Homework Statement



2 = x+2 over x-6


Homework Equations





The Attempt at a Solution



So, multiply both sides by 2 right?

For some reason I am not getting what my book says is right. The end answer is x = 14

I must be doing a step wrong. Can someone show me the steps involved here?

Thanks :)
 
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nukeman said:

The Attempt at a Solution



So, multiply both sides by 2 right?
How would that help you? What could you multiply by on both sides to get rid of that fraction?
 
2=(x+2)/(x-6)

Maybe it would help if you think of each as a variable. So consider

T = M/N

How would you go about moving N to the T side to eliminate the fraction? You would multiply it both sides of the equation so that:
NT = MN/N canceling out the right N's leaving:
NT = M

Consider the expressions in the parenthesis as it's own little group.
 
nukeman said:

Homework Statement



2 = x+2 over x-6

Homework Equations


The Attempt at a Solution



So, multiply both sides by 2 right?
No, I can't imagine why you would think that.

For some reason I am not getting what my book says is right. The end answer is x = 14

I must be doing a step wrong. Can someone show me the steps involved here?

Thanks :)
Well if x= 14, then x+ 2= 16 and x- 2= 12. 16/12= 8/3, not 2. Where did you get x= 14 as the answer?
 
HallsofIvy said:
No, I can't imagine why you would think that.


Well if x= 14, then x+ 2= 16 and x- 2= 12. 16/12= 8/3, not 2. Where did you get x= 14 as the answer?
The denominator is x - 6, not x - 2. If x = 14, the numerator is 16, and the denominator is 8, so when x = 14, (x + 2)/(x - 6) = 2.
 
Here's a weird way to solve it.[tex]\frac{x+2}{x-6}=\frac{x-6+6+2}{x-6}=\frac{x-6}{x-6}+\frac{8}{x-6}=1+\frac{8}{x-6}[/tex]
 
Ok, let's do this one. Can someone please help with this?

If f(x) = 2, solve for x

x+1 over x+2

The right answer is x = -3 I am not sure how to get -3 from that??

Thanks so much guys!
 
We can't just tell you. You have to try it yourself first. Have you read QuarkCharmer's post above? It shows you the first step you need to take.
 

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