How do you graph the inequality # -6 <x + 3 < 6 #?

1 Answer
Oct 2, 2017

Answer:

See a solution process below:

Explanation:

First, we need to solve to #x#. Subtract #color(red)(3)# from each segment of the system of inequalities to solve for #x# while keeping the system balanced:

#-6 - color(red)(3) < x + 3 - color(red)(3) < 6 - color(red)(3)#

#-9 < x + 0 < 3#

#-9 < x < 3#

Or

#x > -9# and #x < 3#

To graph this we will draw vertical lines at #-9# and #3# on the horizontal axis.

The lines will be a daashed because the inequality operators do not contain an "or equal to" clause.

We will shade between the two lines:

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