Question 1203082
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Solve for x, assuming a, b and c are negative constants.

(a) ax + b < c

(b) (ax +b)/c <= b
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<pre>
(a)     <U>Step by step</U>


    Starting inequality to solve is 

        ax + b < c.


    Subtract "b" from both side.  You will get

        ax < c - b.


    Divide both sides by "a".  Since "a" is negative (given), change the sign 
    of the inequality to the opposite one.  You will get

        x > {{{(c-b)/a}}}.    <U>ANSWER</U>



(b)       <U>Step by step</U> 


     Starting inequality is 

         {{{(ax +b)/c}}} <= b.


     Multiply both sides by "c".  Since "c" is negative number, change the sign of the inequality 
     to the opposite one.  You will get

          ax + b >= bc.


     Next, subtract "b" from both sides of the last inequality.  You will get

          ax >= bc - b.


     Now divide both sides by "a".  Since "a" is negative number, change the sign of the inequality 
     to the opposite one.  You will get

          x <= {{{(bc-b)/a}}} = {{{b*(c-1)/a)}}}.


     <U>Answer</U>.  x <= {{{(bc-b)/a}}},  or, equivalently, x <= {{{b*(c-1)/a)}}}.
</pre>

Solved in full, &nbsp;with explanations.


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In writing Math, do not use this mixed combination of words and symbols  " < or = ",
as it was in your post originally (before I fixed it).


Instead, use the symbol " <= ".