Solving Linear Equations with Fractions

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Discussion Overview

The discussion revolves around solving linear equations that involve fractions. Participants explore methods for eliminating denominators and simplifying equations, with a focus on specific examples and procedural approaches.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant suggests that multiplying through by a common denominator can eliminate fractions in the equation $$\frac{y}{5}+\frac{7}{20}=\frac{5-y}{4}$$.
  • Another participant confirms that multiplying the equation by 20, the least common multiple of the denominators, is a valid approach.
  • There is a procedural discussion on expanding and rearranging the equation after eliminating the denominators, leading to the equation $$4y+7=25-5y$$.
  • Participants engage in verifying the steps taken to isolate the variable, arriving at the solution $$y=2$$.
  • Expressions of gratitude are shared, indicating appreciation for the collaborative assistance in understanding the problem-solving process.

Areas of Agreement / Disagreement

Participants generally agree on the method of eliminating denominators and the subsequent steps to solve the equation, although some procedural details are reiterated without explicit consensus on all methods discussed.

Contextual Notes

Some steps in the mathematical reasoning are repeated or paraphrased, which may lead to slight variations in understanding the process. The discussion does not resolve all potential methods for solving similar equations.

Who May Find This Useful

Students seeking help with solving linear equations involving fractions, as well as those interested in collaborative problem-solving approaches in mathematics.

ai93
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If I have a similar question $$\frac{y}{5}+\frac{7}{20}=\frac{5-y}{4}$$ should I go about the same process as the http://mathhelpboards.com/pre-algebra-algebra-2/solve-following-equation-12605.html? Try and cancel out the denominators of 5, 20 and 4? Which would be 20? So times the equation by 20?
 
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yep and that would get rid of the denominator 4y+7=5(5-y)
 
mathsheadache said:
If I have a similar question $$\frac{y}{5}+\frac{7}{20}=\frac{5-y}{4}$$ should I go about the same process as the http://mathhelpboards.com/pre-algebra-algebra-2/solve-following-equation-12605.html? Try and cancel out the denominators of 5, 20 and 4? Which would be 20? So times the equation by 20?

I have moved this question into its own thread. We ask that new questions not be tagged onto existing threads, rather we ask that a new thread be started for a new question. This keeps threads from becoming convoluted and hard to follow. :D
 
ineedhelpnow said:
yep and that would get rid of the denominator 4y+7=5(5-y)

Understood that part, so from here expand to get $$4y+7=25-5y?$$ Move like terms together so, $$4y+5y=25-7?$$ $$\therefore9Y=18. y=2?! $$ :D
 
yep
 
mathsheadache said:
Understood that part, so from here expand to get $$4y+7=25-5y?$$ Move like terms together so, $$4y+5y=25-7?$$ $$\therefore9y=18\implies y=2?! $$ :D

Yes, that's correct. :D
 
Thank you guys, I have learned so much from your help. I would still be stuck on those questions if it wasn't for your help and this forum! :D
 

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