x + 109 = x + 89

- x - x

109 = 89 , but 109 ≠ 89

I don't understand how to do the question.

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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

David M. | Math Tutor in Many Areas.Math Tutor in Many Areas.

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