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

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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)

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

|4x – 3| – 1 > 12

First add 1 on both sides

By adding, you should get

|4x - 3| > 13 Since there are absolute value signs change your equation into

4x - 3 > 13  and 4x - 3 < -13 now add 3 on both sides to both equation

By adding, you should get

4x > 16   and 4x < -10 now divide 4 on both sides

By dividing, you should get

x > 4   and  x < -10/4

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