How do you solve and graph #abs(n+2)>=1#?

1 Answer
smendyka
Dec 19, 2017

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

#-1 >= n + 2 >= 1#

Subtract #color(red)(2)# from each segment of system of equations to solve for #n# while keeping the system balanced:

#-1 - color(red)(2) >= n + 2 - color(red)(2) >= 1 - color(red)(2)#

#-3 >= n + 0 >= -1#

#-3 >= n >= -1#

Or

#n <= -3#; #n >= -1#

Or, in interval notation:

#(-oo, -3]#; #[-1, +oo)#

To graph this we will draw a vertical lines at #-3# and #-1# on the horizontal axis.

The lines will be a solid lines because the inequality operators contain an "or equal to" clause.

We will shade to the left and right of the lines to show the intervals:

enter image source here

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