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x+109=x+89

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4 Answers

I believe, the best answer will be: given equation does not have any solutions, because for any value of x we will get 109 = 89 , which is false statement. 

   x + 109 = x + 89 
 - x           - x  

     109 = 89 , but 109 ≠ 89 
Without any algebra, it is not possible for 109 added to a number to be the same as 89 added to the same number. 
If you need a proof, I will show that if a+b=a+c then b=c
b=b+0            definition of 0
  =b+(a+(-a)) every number has an additive inverse
  =(b+a) +(-a) associative law of addition
  =(a+b) +(-a) addition is commutative
  =(a+c) +(-a) by hypothesis
  =(c+a) +(-a) addition is commutative
  = c+(a+(-a)) associative law of addition
  =c+0            definition of additive inverse
  =c                since 0 is neutral element for addition
Hi Haylie;
x+109=x+89
Is it possible that this is...
x+109=3x+89
?????
I will resolve...
x+109=3x+89
Let's subtract x from both sides...
-x+x+109=3x+89-x
109=2x+89
Let's subtract 89 from both sides...
-89+109=2x+89-89
20=2x
Let's divide both sides by 2...
20/2=(2x)/2
10=x
 
Let's check our work...
x+109=3x+89
10+109=[(3)(10)]+89
119=30+89
119=119
The best answer here would be x=+/-infinity because infinity +109 and infinity +89 are both equal to infinity.