Question 142989
{{{abs(x+3/4)<1/4}}} Start with the given inequality



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


{{{x+3/4 > -1/4}}} and {{{x+3/4 < 1/4}}} Break up the absolute value inequality using the given rule



{{{-1/4 < x+3/4 < 1/4}}} Combine the two inequalities to get a compound inequality



{{{cross(4)(-1/cross(4)) < 4(x+3/cross(4)) < cross(4)(1/cross(4))}}} Multiply all sides by the LCD 4 to clear the fractions



{{{-1<4x+3<1}}} Distribute and multiply


{{{-4 < 4x < -2}}} Subtract 3 from  all sides



{{{-1 < x < -1/2}}}  Divide all sides by 4 and reduce to isolate x




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Answer:


So our answer is


{{{-1 < x < -1/2}}}




which looks like this in interval notation



*[Tex \LARGE \left(-1,-\frac{1}{2}\right)]