How do you graph and solve #|x + 4| <= 6#?

1 Answer
smendyka
Oct 16, 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.

We can solve the problem using this system of inequalities:

#-6 <= x + 4 <= 6#

#-6 - color(red)(4) <= x + 4 - color(red)(4) <= 6 - color(red)(4)#

#-10 <= x + 0 <= 2#

#-10 <= x <= 2#

Or

#x >= 10# and #x <= 2#

Or, in interval notation:

#[-10, 2]#

To graph this we will draw two vertical lines at #-10# and #2# on the horizontal axis.

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

We will shade between the lines because the interval notation shows a space between the two lines:

enter image source here

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