How do you solve and graph #abs(w-2)<2#?

1 Answer
smendyka
Oct 22, 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.

#-2 < w - 2 < 2#

#-2 + color(red)(2) < w - 2 + color(red)(2) < 2 + color(red)(2)#

#0 < w - 0 < 4#

#0 < w < 4#

Or

#x > 0# and #w < 4#

Or, in interval notation:

#(0, 4)#

To graph this we will draw two vertical lines at #0# and #4# on the horizontal axis.

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

We will shade between the two lines to capture the interval solution:

enter image source here

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