(a)     Step by step


    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 > .    ANSWER



(b)       Step by step 


     Starting inequality is 

          <= 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 <=  = .


     Answer.  x <= ,  or, equivalently, x <= .