Question 7779
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.