SOLUTION: 9. Solve {{{abs(x-1/4)<1/2}}}

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Question 143740: 9. Solve abs%28x-1%2F4%29%3C1%2F2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x-1%2F4%29%3C1%2F2 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-1%2F4+%3E+-1%2F2 and x-1%2F4+%3C+1%2F2 Break up the absolute value inequality using the given rule


-1%2F2+%3C+x-1%2F4+%3C+1%2F2 Combine the two inequalities to get a compound inequality


4%28-1%2Fcross%282%29%29+%3C+4%28x-1%2Fcross%284%29%29+%3C+4%281%2Fcross%282%29%29 Multiply all sides by the LCD 4 to clear the fractions


-2%3C4x-1%3C2 Distribute and multiply


-1%3C4x%3C3 Add 1 to all sides


-1%2F4%3Cx%3C3%2F4 Divide every side by 4 to isolate x.



So the solution is

-1%2F4%3Cx%3C3%2F4

which looks like in interval notation.