How do you solve #abs(x+1)<7#?

1 Answer
smendyka
Feb 27, 2017

See the entire solution process below:

Explanation:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. For inequalities we solve this as:

#-7 < x + 1 < 7#

Now, subtract #color(red)(1)# from each segment of the system of inequalities to solve for #x# while keeping the system balanced:

#-7 - color(red)(1) < x + 1 - color(red)(1) < 7 - color(red)(1)#

#-8 < x + 0 < 6#

#-8 < x < 6#

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