Question 143740

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.