What is the solution set of |4x – 3| – 1 > 12?

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l 4x-3 l -1 > 12

First we will add 1 to both sides.

==> l 4x-3 l > 13

Now by definition we will rewrite:

==> 4x-3 > 13 OR 4x-3 < -13

We will solve both cases:

==> 4x-3 > 13

==> 4x > 16

==> x > 4 ............(1)

==> 4x-3 < -13

==> 4x < -10

==> x < -10/4

==> x < -5/2 ............(2)

Then the solution is :

x belongs to ( -inf, -5/2) U (4, inf)

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What is the solution set of |4x – 3| – 1 > 12?

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