Question 362872

{{{6(7n-4)<=-6n+24}}} Start with the given inequality.



{{{42n-24<=-6n+24}}} Distribute.



{{{42n<=-6n+24+24}}} Add {{{24}}} to both sides.



{{{42n+6n<=24+24}}} Add {{{6n}}} to both sides.



{{{48n<=24+24}}} Combine like terms on the left side.



{{{48n<=48}}} Combine like terms on the right side.



{{{n<=(48)/(48)}}} Divide both sides by {{{48}}} to isolate {{{n}}}. 



{{{n<=1}}} Reduce.



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Answer:


So the solution is {{{n<=1}}} 




So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-\infty,1}]<font size="8">]</font>




Also, the answer in set-builder notation is  *[Tex \LARGE \left\{n\|n\le1\right\}]



Here's the graph of the solution set


{{{drawing(500,80,-9, 11,-10, 10,
number_line( 500, -9, 11),


arrow(1,0,-9,0),
arrow(1,0.30,-9,0.30),
arrow(1,0.15,-9,0.15),
arrow(1,-0.15,-9,-0.15),
arrow(1,-0.30,-9,-0.30),




circle(1,0,0.2),
circle(1,0,0.15),
circle(1,0,0.1),
circle(1,0,0.2-0.02)
)}}}


Note: there is a closed circle at n=1



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