SOLUTION: what are the real values of x that are solutions for the inequality |x-2|_< 6

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Question 207603: what are the real values of x that are solutions for the inequality |x-2|_< 6
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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abs%28x-2%29%3C6 implies that:
(x-2) < 6
and (x-2) > (-6)
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solving (x-2) < 6 first:
x-2 < 6
add 2 to both sides of the equation to get:
x < 8
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solving (x-2) > (-6)
x-2 > -6
add 2 to both sides to get:
x > -4
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your answer is:
x < 8 and x > -4
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this can be written as:
-4 < x < 8
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to prove, substitute in your original equation:
abs%28x-2%29%3C6
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if x = 8, equation becomes abs%288-2%29+%3C+6 which becomes abs%286%29+%3C+6 which becomes 6+%3C+6 which would not satisfy the equation because x is not smaller than 8.
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if x = 7 equation becomes abs%287-2%29+%3C+6 which becomes abs%285%29+%3C+6 which becomes 5+%3C+6 which would satisfy the equation because x is smaller than 8 as required.
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if x = -4, equation becomes abs%28-4-2%29+%3C+6 which becomes abs%28-6%29+%3C+6 which becomes 6+%3C+6 which would not satisfy the equation because x is not larger than -4.
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if x = -3, equation becomes abs%28-3-2%29+%3C+6 which becomes abs%28-5%29+%3C+6 which becomes 5+%3C+6 which would satisfy the equation because x is larger than -4 as required.
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