SOLUTION: 6|9b-1|-4 > 2 Solve each inequality and graph its solution. Thanks!

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Question 1122819: 6|9b-1|-4 > 2 Solve each inequality and graph its solution. Thanks!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
6abs%289b-1%29-4%3E2
6abs%289b-1%29%3E6
abs%289b-1%29%3E1

system%289b-1%3E1%2COR%2C1-9b%3E1%29
-
b%3E1%2F9
OR
-9b%3E0
b%3C0
-

system%28b%3C0%2COR%2Cb%3E1%2F9%29
<============()------------------------()=======================>
              0                      1%2F9


Answer by ikleyn(52894) About Me  (Show Source):
You can put this solution on YOUR website!
.
6|9b-1|-4 > 2 Solve each inequality and graph its solution. Thanks!
~~~~~~~~~~~~~~~~~~~~~~~~~~~

6|9b-1|-4 > 2    ====>  add 4 to both sides  ====>


6|9b-1| > 6   ====>  divide both sides by 6  ====>


|9b-1| > 1  ====>  is equivalent to


9%2Aabs%28b-1%2F9%29 > 1  ====>  divide both sides by 9  ====>


abs%28b-1%2F9%29 > 1%2F9.


The solution for the last inequality are ALL THOSE x that are remoted farther than  1%2F9  from the point  b = 1%2F9.


In other words, the solution set is  the union of two semi-infinite intervals  b < 0  and  b > 2%2F9.


Answer.  The solution set is  the union of two semi-infinite intervals  b < 0  and  b > 2%2F9,  

         or, in the interval form,  the union  (-infinity,0) U (2%2F9,infin+ity).

Solved.

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On solving inequalities,  see introductory lessons
    - Solving simple and simplest linear inequalities
    - Solving absolute value inequalities (*)
in this site.   Especially lesson  (*)  of these two.

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Be aware ! :   The solution by  @josgarithmetic is   W R O N G.