SOLUTION: Solve {{{abs((2x-1)/3)>=5/6}}}

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Question 142990: Solve abs%28%282x-1%29%2F3%29%3E=5%2F6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28%282x-1%29%2F3%29%3E=5%2F6 Start with the given inequality


Break up the absolute value (remember, if you have abs%28x%29%3E=a, then x+%3C=+-a or x+%3E=+a)

%282x-1%29%2F3+%3C=+-5%2F6 or %282x-1%29%2F3+%3E=5%2F6 Break up the absolute value inequality using the given rule



6%28%282x-1%29%2Fcross%283%29%29+%3C=+6%28-5%2Fcross%286%29%29 or 6%28%282x-1%29%2Fcross%283%29%29+%3E=+6%285%2Fcross%286%29%29 Multiply both sides by the LCD 6 to clear the fractions


2%282x-1%29+%3C=+-5 or 2%282x-1%29+%3E=+5 Distribute and multiply


4x-2+%3C=+-5 or 4x-2+%3E=+5 Distribute again


x%3C=+-3%2F4 or x+%3E=+7%2F4 Isolate x in each case



So our solution is


x%3C=+-3%2F4 or x+%3E=+7%2F4



which looks like this in interval notation

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