SOLUTION: Solve the inequality |x - 1/2| > or = 2/3.

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Question 39207: Solve the inequality |x - 1/2| > or = 2/3.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+abs%28x+-+%281%2F2%29%29+%3E=+2%2F3+ means we have 2 possibilities since the |.| part is like a V-shape, ie 2 straight lines. Mathematically we have to solve:

+%28x+-+%281%2F2%29%29+%3E=+2%2F3+ and +-%28x+-+%281%2F2%29%29+%3E=+2%2F3+

First: +%28x+-+%281%2F2%29%29+%3E=+2%2F3+
+%28x+-+%283%2F6%29%29+%3E=+4%2F6+
+x+%3E=+4%2F6+%2B+3%2F6+
+x+%3E=+7%2F6+

and now: +-%28x+-+%281%2F2%29%29+%3E=+2%2F3+
+-x+%2B+%281%2F2%29+%3E=+2%2F3+
+-x+%2B+%283%2F6%29+%3E=+4%2F6+
+-x+%3E=+4%2F6+-+3%2F6+
+-x+%3E=+1%2F6+
+x+%3C=+-1%2F6+

So, the value of x needs to be "less than or equal to" (-1/6) OR "greater than or equal to" (7/6)

Graphically, we can show this as +graph%28300%2C300%2C-2%2C3%2C-2%2C3%2Cabs%28x+-+%281%2F2%29%29%2C+%282%2F3%29%29+, where i have plotted both +y+=+abs%28x+-+%281%2F2%29%29+ and +y+=+2%2F3+. Where they cross each other are the 2 answers i calculated

jon.