How do you solve and graph #-5<=-n-6<=0#?

1 Answer
May 7, 2017

Answer:

See a solution process below:

Explanation:

First, add #color(red)(6)# to each segment of the system of inequalities to isolate the #n# term while keeping the system balanced:

#-5 + color(red)(6) <= -n - 6 + color(red)(6) <= 0 + color(red)(6)#

#1 <= -n - 0 <= 6#

#1 <= -n <= 6#

Now, multiply each segment by #color(blue)(-1)# to solve for #n# while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we need to reverse the inequality operators:

#color(blue)(-1) * 1 color(red)(>=) color(blue)(-1) * -n color(red)(>=) color(blue)(-1) * 6#

#-1 color(red)(>=) n color(red)(>=) -6#

Or

#n <= -1#; #n >= -6#

Or, in interval notation:

#[-6, -1]#