Question 1122819
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6|9b-1|-4 > 2      Solve each inequality and graph its solution. Thanks!
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<pre>
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*abs(b-1/9)}}} > 1  ====>  divide both sides by 9  ====>


{{{abs(b-1/9)}}} > {{{1/9}}}.


The solution for the last inequality are ALL THOSE x that are remoted farther than  {{{1/9}}}  from the point  b = {{{1/9}}}.


In other words, the solution set is  the union of two semi-infinite intervals  b < 0  and  b > {{{2/9}}}.


<U>Answer</U>.  The solution set is  the union of two semi-infinite intervals  b < 0  and  b > {{{2/9}}},  

         or, in the interval form,  the union  ({{{-infinity}}},{{{0}}}) U ({{{2/9}}},{{{infin ity}}}).
</pre>

Solved.


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On solving inequalities, &nbsp;see introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-simple-and-simplest-inequalities.lesson>Solving simple and simplest linear inequalities</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-absolute-value-inequalities-IK.lesson>Solving absolute value inequalities</A> (*)

in this site.  &nbsp;&nbsp;Especially lesson &nbsp;(*) &nbsp;of these two.


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<U>Be aware !</U> :  &nbsp;&nbsp;The solution by &nbsp;@josgarithmetic is &nbsp;&nbsp;<U>W R O N G</U>.