SOLUTION: How do you find the answer for the absolute value of |6x-13|=3?

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Question 12681: How do you find the answer for the absolute value of |6x-13|=3?
Answer by AdolphousC(70) About Me  (Show Source):
You can put this solution on YOUR website!
Since the absolute value of a number is the POSTIVE DISTANCE FROM ZERO, you can really have two answers |3| = 3 and |-3|=3


Therefor the expression inside the absolute value bars can equal either 3 or -3, so you need to set up two separate expresstions representing that fact.


Expression 1
+6x+-+13+=+3+
Add 13 to both sides
+6x+=+16+
Divide by 6
+x+=+16%2F6+
reduce
+x+=+8%2F3+


Expression 2
+6x+-+13+=+-3+
Add 13 to both sides
+6x+=+10+
Divide by 6
+x+=+10%2F6+
reduce
+x+=+5%2F3+


So either answer will work, if you plug in the Expression 1, you will get
|3| which is 3, if you plug in Expression 2, you will get |-3| which is ALSO 3