SOLUTION: The solution set of [x-6]=4 is______. -2 or 2 -2 or 10 2 or -10 2 or 10

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Question 174312: The solution set of [x-6]=4 is______.

-2 or 2
-2 or 10
2 or -10
2 or 10

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%28x-6%29=4 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=-4 or x-6=4 Set the expression x-6 equal to the original value 4 and it's opposite -4




Now lets focus on the first equation x-6=-4


x=-4%2B6Add 6 to both sides


x=2 Combine like terms on the right side






Now lets focus on the second equation x-6=4



x=4%2B6Add 6 to both sides


x=10 Combine like terms on the right side




=========================================================

Answer:


So the solutions are:

x=2 or x=10



Notice if we graph y=abs%28x-6%29 and y=4 (just set each side equal to y and graph), we get


Graph of y=abs%28x-6%29 (red) and y=4(green)

and we can see the two graphs intersect at x=2 and x=10. So this verifies our answer.