Question 221450

{{{(1/2)n-1/8>3/4+(5/6)n}}} Start with the given inequality.



{{{24((1/cross(2))n-1/cross(8))>24(3/cross(4)+(5/cross(6))n)}}} Multiply both sides by the LCD {{{24}}} to clear any fractions.



{{{12n-3>18+20n}}} Distribute and multiply.



{{{12n>18+20n+3}}} Add {{{3}}} to both sides.



{{{12n-20n>18+3}}} Subtract {{{20n}}} from both sides.



{{{-8n>18+3}}} Combine like terms on the left side.



{{{-8n>21}}} Combine like terms on the right side.



{{{n<(21)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{n}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{n<-21/8}}} Reduce.



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Answer:


So the solution is {{{n<-21/8}}} which in decimal form is {{{n<-2.625}}}