Question 164315
{{{2n+5>11-n}}} Start with the given inequality.



{{{2n>11-n-5}}} Subtract {{{5}}} from both sides.



{{{2n+n>11-5}}} Add {{{n}}} to both sides.



{{{3n>11-5}}} Combine like terms on the left side.



{{{3n>6}}} Combine like terms on the right side.



{{{n>(6)/(3)}}} Divide both sides by {{{3}}} to isolate {{{n}}}. 



{{{n>2}}} Reduce.



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Answer:


So the answer is {{{n>2}}}




So the answer in interval notation is *[Tex \LARGE \left(2,\infty\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{n\|n>2\right\}]



Check:


To check the answer, simply plug in a value that is greater than 2 (say 3)


{{{2n+5>11-n}}} Start with the given inequality.



{{{2(3)+5>11-3}}} Plug in n=3



{{{6+5>11-3}}} Multiply



{{{11>8}}} Combine like terms. Since the inequality is true, this verifies our answer.



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Here's the graph of the solution set


{{{drawing(500,80,-8, 12,-10, 10,
number_line( 500, -8, 12),

arrow(2,0,12,0),
arrow(2,0.30,12,0.30),
arrow(2,0.15,12,0.15),
arrow(2,-0.15,12,-0.15),
arrow(2,-0.30,12,-0.30),

circle(2,0,0.3),
circle(2,0,0.3),
circle(2,0,0.3),
circle(2,0,0.3-0.02)
)}}}


Take note of the open circle at n=2. This tells us to exclude the endpoint.