Question 753715
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What is the number line graph of |6-(2x-3)|>9 
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<pre>
The given inequality

    |6 - (2x-3)| > 9


is the same as

    |-2x + 9| > 9


and is equivalent to

    |x - 4.5| > 4.5.


It describes the points x on number line that are remoted MORE THAN 4.5 units from the point 4.5.


The solution set (these points) are  

    x < 0  or  x > 9,               <U>ANSWER</U>


or, in the interval notation, the solution set is the union  

    (-oo,0) U (9,oo).               <U>ANSWER</U>
</pre>

Solved.


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On solving absolute value inequalities, see my lesson

&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.


Consider this lesson as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.
Read it attentively and learn how to solve this type of problems once and for all.



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Ignore the solution / (the response) from  &nbsp;@CubeyThePenguin, &nbsp;since it is &nbsp;TOTALLY &nbsp;WRONG.