What is the solution set for #abs(x – 6) = 10#?

1 Answer
Joel Kindiak
Aug 8, 2015

#{x : x \in \RR, x = –4, 16}#

Explanation:

Consider that given every #abs(x) = c#, only two #x#'s fit the bill: #c# or #-c#. Apply that principle here:

#abs(x - 6) = 10#
#\Rightarrow# #x - 6 = 10# or #x - 6 = –10#
#\Rightarrow# #x = 16# or #x = –4#

To express answer in set notation, we use curly brackets and set-builder notation:

#{x : x \in \RR, x = –4, 16}#

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