A+2b=2a+b=>1=2. please tell me what is the problem

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Discussion Overview

The discussion revolves around the algebraic manipulation of the equation a + 2b = 2a + b, leading to the conclusion 1 = 2. Participants are exploring the implications of their calculations and identifying potential errors in reasoning, particularly regarding division by zero and the conditions under which certain algebraic laws apply.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a series of algebraic steps leading to the conclusion 1 = 2, expressing confusion about the error in their reasoning.
  • Another participant questions whether the implication of 2 * 0 = 3 * 0 leads to the conclusion that 2 = 3, suggesting a possible parallel to the original problem.
  • A different participant provides an alternative manipulation of the equation, concluding that a = b, and highlights the issue of dividing by zero when a - b = 0.
  • Another participant notes that the law ax = bx implies a = b only if x is nonzero, emphasizing the importance of this condition in the reasoning process.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the algebraic manipulations and the implications of division by zero. There is no consensus on a single resolution to the problem presented.

Contextual Notes

Participants highlight the importance of nonzero conditions in algebraic laws and the potential pitfalls of manipulating equations that involve zero. The discussion remains focused on the implications of these mathematical principles without reaching a definitive conclusion.

Who May Find This Useful

Individuals interested in algebra, mathematical reasoning, and the implications of division by zero may find this discussion relevant.

waqarrashid33
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if we get:

a+2b=2a+b
=>a-b=2a-2b
=>a-b=2(a-b)
=>1=2

I can't figure out the problem in it..please tell me
 
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Does 2*0=3*0 also imply 2=3??
 
waqarrashid33 said:
if we get:

a+2b=2a+b
So 2b- b= 2a- a which gives a= b.

=>a-b=2a-2b
=>a-b=2(a-b)
=>1=2
Since a= b, a- b= 0 and you cannot divide by 0.0

I can't figure out the problem in it..please tell me
 
Note that the law

ax=bx~\Rightarrow~a=b

Only holds if x is nonzero!

The correct way in solving this is

ax=bx~\Rightarrow~ ax-bx=0~\Rightarrow~(a-b)x=0~\Rightarrow ~a-b=0~\text{or}~x=0
 

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