Question 1180732
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<pre>

The given inequality  | 7x-3 | <= 18  means that  <U>BOTH THESE TWO inequalities are valid</U>


    7x - 3 <= 18    (1)

AND

    -(7x-3) <= 18   (2)



Inequality (1) implies that

    7x <= 18 + 3 = 21,  x <= 3.



Inequality (2) implies that

    -7x <= 18 - 3 = 15,  7x >= -15  (notice that I changed the sign in both sides 
                                     and changed the inequality sign for the opposite one),   

                                    x >= {{{-15/7}}}.


So, the final answer is  the INTERSETION of both partial solution sets  {{{-15/7}}} <= x <= 3.
</pre>

Solved and explained.


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To see many other similar and different SOLVED problems on absolute value equations, &nbsp;look into the 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.