How do you solve #abs(x-16)<10#?

1 Answer
smendyka
Nov 15, 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.

#-10 < x - 16 < 10#

First, add #color(red)(16)# to each segment of the system of inequalities to solve for #x# while keeping the system balanced:

#-10 + color(red)(16) < x - 16 + color(red)(16) < 10 + color(red)(16)#

#6 < x - 0 < 26#

#6 < x < 26#

Or

#x > 6# and #x < 26#

Or, in interval notation

#(6, 26)#

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