What is the solution set for #abs(x – 6) + 3 < 10#?

1 Answer
Bill K.
Aug 10, 2015

#-1 < x < 13#

Explanation:

First, subtract 3 from both sides of the inequality #|x-6|+3 < 10# to get #|x-6| < 7#. Next, note that this inequality implies that #-7 < x-6 < 7#. Finally, add 6 to each part of this line of inequalities to get #-1 < x < 13#.

Another way to think about the inequality #|x-6| < 7# is that you are looking for all #x#-values whose distance to 6 is less than 7. If you draw a number line, that will help you see the answer is #-1 < x < 13#.

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