How do you solve #-3\leq \frac { - 2n - 11} { 3} \leq 1#?

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Answer 1 · 2017-05-06T08:53:54

#-7 <=n <= -1#

Multiply through by #3# to get rid of the fraction.

#-3 color(red)(xx3) <= (color(red)(cancel3xx)(-2n-11))/cancel3 <= 1color(red)(xx3)#

#-9 <=-2n-11 <=3#

Solve as two separate inequalities:

#-9<=-2n-11color(white)(mmmm)-2n-11 <= 3#

#2n <= -11+9color(white)(mmmmm)-11-3 <= 2n#

#2n <=-2color(white)(mmmmmmmm)-14 <=2n#

#n<=-1color(white)(mmmmmmmkm)-7<= n#

Combine into one inequality.

#n# is bigger than (or equal to) #-7#, but smaller than (or equal to) #-1#

#-7 <=n <= -1#