For all integers a, b, and c, if a+b=a+c then b=c?

Question

I need help proving that this is fact.

I have tried doing it this way:

a+b=a+c

a+b+(-a)=a+c+(-a)

0+b=0+c

b=c

but these seems to simple... am I doing something wrong here?

Answer 1

5+3=5+4

b and c could be anything.

b=c is false

Answer 2

No, that's all the proof you need.

Answer 3

You did it right. Good job!

Answer 4

No you're right. If a=a and a+b=a+c then b would have to =c

Answer 5

Umm...

a + b = a + c

Cancel the a's on both sides... or...

a - a = -b + c

0 = -b + c

b = c

I hope that helps. :)

me07.

Answer 6

You got it right, Kelly ... there are times when mathematical proofs can be done in a very simple and straightforward manner.

  

Answer 7

Yes, it is that simple.

You have provided a logical sequence of steps that prove that b = c.  Good job!

Answer 8

No, you are right and it is simple.

Answer 9

It is that simple, or more accurately- it *can* be that simple.

If you're in a pre-college class (algebra), you answer is both correct and sufficient.  I took a logic class in college which requires more complicated proving.

Don't worry- you're probably just better at math than most kids- some people find this answer unintuitive.  Be happy about your fortune and try something more challenging by flipping forward in your textbook!

Answer 10

no you are right

Answer 11

You proof is exactly right ! congratulation !

Answer 12

no it is correct. Just because it is simple does not make it incorrect.