Question 143740
{{{abs(x-1/4)<1/2}}} Start with the given inequality



Break up the absolute value (remember, if you have {{{abs(x)< a}}}, then {{{x > -a}}} and {{{x < a}}})


{{{x-1/4 > -1/2}}} and {{{x-1/4 < 1/2}}} Break up the absolute value inequality using the given rule



{{{-1/2 < x-1/4 < 1/2}}} Combine the two inequalities to get a compound inequality



{{{4(-1/cross(2)) < 4(x-1/cross(4)) < 4(1/cross(2))}}} Multiply all sides by the LCD 4 to clear the fractions



{{{-2<4x-1<2}}} Distribute and multiply



{{{-1<4x<3}}} Add 1 to all sides



{{{-1/4<x<3/4}}} Divide every side by 4 to isolate x. 




So the solution is


{{{-1/4<x<3/4}}} 


which looks like *[Tex \LARGE \left(-\frac{1}{4},\frac{3}{4}\right)] in interval notation.