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

  • Context: Undergrad 
  • Thread starter Thread starter waqarrashid33
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the algebraic manipulation of the equation a + 2b = 2a + b, leading to the erroneous conclusion that 1 = 2. The critical error arises from dividing by zero when simplifying a - b = 2(a - b) under the assumption that a = b. The correct interpretation emphasizes that the equality ax = bx only holds when x is nonzero, highlighting the necessity of avoiding division by zero in algebraic proofs.

PREREQUISITES
  • Understanding of algebraic equations and manipulations
  • Knowledge of the properties of equality in mathematics
  • Familiarity with the concept of division by zero and its implications
  • Basic skills in solving linear equations
NEXT STEPS
  • Study the implications of dividing by zero in algebraic contexts
  • Learn about the properties of equality and their applications in proofs
  • Explore advanced algebraic techniques for solving equations
  • Review examples of common algebraic mistakes and their corrections
USEFUL FOR

Students, educators, and anyone interested in improving their understanding of algebraic principles and avoiding common mathematical errors.

waqarrashid33
Messages
76
Reaction score
0
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
 
Mathematics news on Phys.org
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
 

Similar threads

High School Complete the square, yes, but what does it mean?
  • · Replies 19 ·
Replies
19
Views
3K
MHB 1.1.21 simplify rational expression
  • · Replies 14 ·
Replies
14
Views
2K
Find the values of a and b to get max/min of certain expression
  • · Replies 21 ·
Replies
21
Views
3K
High School Doing proofs: Setting an expression as a variable
  • · Replies 3 ·
Replies
3
Views
1K
MHB Possibilities for the side and angle of the triangle
  • · Replies 10 ·
Replies
10
Views
3K
High School Expressions of ##log(a+b), tan^{-1}(a+b),sin^{-1}(a+b)##,etc
  • · Replies 12 ·
Replies
12
Views
2K
MHB Inequality Challenge V: Prove $(a+b)^{a+b} \le (2a)^a(2b)^b$
  • · Replies 3 ·
Replies
3
Views
1K
MHB Solving for Common Root in $(1)$ and $(2)$
  • · Replies 1 ·
Replies
1
Views
1K
High School Is Each Stage of Pascal's Triangle Special?
  • · Replies 11 ·
Replies
11
Views
2K
Find the value of ##a, b## and ##k## in the problem involving graphs
  • · Replies 6 ·
Replies
6
Views
2K