SOLUTION: Solve {{{abs(x+3/4)<1/4}}}

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Question 142989: Solve abs%28x%2B3%2F4%29%3C1%2F4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x%2B3%2F4%29%3C1%2F4 Start with the given inequality


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

x%2B3%2F4+%3E+-1%2F4 and x%2B3%2F4+%3C+1%2F4 Break up the absolute value inequality using the given rule


-1%2F4+%3C+x%2B3%2F4+%3C+1%2F4 Combine the two inequalities to get a compound inequality


Multiply all sides by the LCD 4 to clear the fractions


-1%3C4x%2B3%3C1 Distribute and multiply

-4+%3C+4x+%3C+-2 Subtract 3 from all sides


-1+%3C+x+%3C+-1%2F2 Divide all sides by 4 and reduce to isolate x



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Answer:

So our answer is

-1+%3C+x+%3C+-1%2F2



which looks like this in interval notation