SOLUTION: [x-6]=2

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Question 281737: [x-6]=2
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%28x-6%29=2 Start with the given equation


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

x-6=-2 or x-6=2 Set the expression x-6 equal to the original value 2 and it's opposite -2




Now lets focus on the first equation x-6=-2


x=-2%2B6Add 6 to both sides


x=4 Combine like terms on the right side






Now lets focus on the second equation x-6=2



x=2%2B6Add 6 to both sides


x=8 Combine like terms on the right side





So the solutions to abs%28x-6%29=2 are:

x=4 and x=8


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the definition of absolute value.




Hence, if , then either



or



Therefore



or



So, 8 minus 6 is 2 and the absolute value of 2 is 2, and the first answer checks. And then 4 minus 6 is minus 2 and the absolute value of minus 2 is 2 -- second answer checks.

John