a-b= -(a-b)

Question

Given

      a-b= -(a-b)

which statement is true

 

a is greater

b is greater

a and b are equal

not enough information

 

I know that the answer is C both a and b are equal, but I do not understand why.

I tried solving for a and came up with a=0, but cannot find an anser for b.

Am I on the right track?

 

Answer 1

Hi Sandy;

a-b=-(a-b)

a-b=-a+b

Let's combine like terms...

Let's subtract a from both sides...

a-a-b=-a-a+b

-b=-2a+b

Let's subtract b from both sides...

-b-b=-2a+b-b

-2b=-2a

Let's divide both sides by -2...

(-2b)/-2=(-2a)/-2

b=a

 

a and b are equal.

Answer 2

If you let x = a-b, then x = -x, and if you solve that for x, you get x = 0.  Whenever something equals its opposite, that something is 0.  Here, that something is a-b, so a-b = 0, which means a = b.