How do you graph and solve #|x-4|-5<1#?

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Answer 1 · 2017-05-20T18:32:43

First add 5 to both sides:

#|x-4| < 6#

This means that #x-4# must be between #-6# and #6#. We can write this mathematically as:

#-6 < x-4 < 6#

Finally, add 4 to all parts of the inequality.

#-2 < x < 10#

This is the final answer. On a number line graph, this inequality would look like this:
enter image source here
(image courtesy of Wolfram Alpha)