Question 7779: This is a great site for help. I have worked my solution for the absolute value below but I would like to know if I am addressing it correctly.
Could you please solve the absolute value equation and explain each step for my reference:
| a – 6 | = | 6 – a |
Thanks
Found 2 solutions by prince_abubu, jam123:
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! It looks like you have to solve 4 different equations for this one, since both sides of the equation contain absolute value quantities.
Case 1: a - 6 = 6 - a
When you combine like terms across the equals sign, you'll end up with 2a = 12, and finally, a = 6.
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Case 2: a - 6 = a - 6
Both sides of the equals sign look exactly alike. In this case, you can pretty much choose whatever value you want for a and the equality will still hold true.
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Case 3: 6 - a = 6 - a
Same as case 2, except it's 6 - a instead of a - 6. You can still pretty much pick any a you want and both sides will be equal.
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Case 4: 6 - a = a - 6
If you try to solve this, eventually, a = 6.
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Cases 1 and 4 showed that a = 6, but cases 2 and 3 show that a can equal anything. Which ones are right then? What is the ultimate answer? Since "a can be anything" does include that a can equal 6, then by all means, a can be any number you want it to be. Try plugging in anything in the original equation will result in equal sides. Although one of may turn out a negative of the other, the absolute value signs guarantee that the negative sign will be "thrown away", thus both sides will be equal.
Answer by jam123(18) (Show Source):
You can put this solution on YOUR website! 6 or -6
6-6 = 6-6 and
6--6 (I moved over -6) = 6--6
Let's try making a to something like 5.
So, 5-6 =/= 6-5.
Is prince_abubu right about the 6-a = 6-a can be possible?
Let's see.
-1=/=1 (the equation above solved)
We'll get the same answer if prince_abubu is right...wait,
if 6-5=6-5
then
1=1!
Wrong answer!
Let's try again.
Let's say that a-6 is -6a and 6-a is 6a.
-6a =/= 6a
BUT
-6a=-6a.
and
6a=6a
Maybe, but I don't think there is an answer to this.
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