How do you solve #|w + 3| < 5#?

1 Answer
smendyka
Feb 8, 2017

See the entire solution process below:

Explanation:

The absolute value function takes any negative or positive term and converts it into its positive form. Therefore we must solve this inequality as a system of inequalities for both the negative and positive form of what the absolute value function is equated to.

We can rewrite #abs(w + 3) < 5# as:

#-5 < w + 3 < 5#

We can now subtract #color(red)(3)# from each part of this system of inequalities to solve for #w# while keeping the system balanced:

#-5 - color(red)(3) < w + 3 - color(red)(3) < 5 - color(red)(3)#

#-8 < w + 0 < 2#

#-8 < w < 2# or

#-8 < w# and #w < 2#

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