Question 149695

{{{abs(5n-2)<2}}} Start with the given inequality



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


{{{5n-2 > -2}}} and {{{5n-2 < 2}}} Break up the absolute value inequality using the given rule



{{{-2 < 5n-2 < 2}}} Combine the two inequalities to get a compound inequality




{{{0 < 5n < 4}}} Add 2 to  all sides



{{{0 < n < 4/5}}}  Divide all sides by 5 to isolate n




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Answer:


So our answer is


{{{0 < n < 4/5}}}




which looks like this in interval notation



*[Tex \LARGE \left(0,\frac{4}{5}\right)]