x+109=x+89

Question

I don't understand how to do the question.

Answer 1

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 

Answer 2

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

Answer 3

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

Answer 4

The best answer here would be x=+/-infinity because infinity +109 and infinity +89 are both equal to infinity.