Question 550068
<pre>
             {{{3/5}}}(3x-3) > 9

Multiply both sides by 5 to clear the fraction.
(The  > symbol does not reverse when we multiply
or divide both sides by a positive number)

        (5)·{{{3/5}}}(3x-3) > (5)·9

            3(3x-3) > 45

             9x - 9 > 45
 
                 9x > 54

Divide both sides by 9.
(The  > symbol does not reverse when we multiply
or divide both sides by a positive number)

                {{{9x/9}}} > {{{54/9}}}
                 
                 x > 6 

To write the solution set in set-builder notation:

             {x | x > 6}      

-----------------------------------------------------


            0.4x + 6 &#8804; 1.2x - 3 
            
Clear of decimals by multiplying through every term by 10              

  (10)·0.4x + (10)·6 &#8804; (10)·1.2x - (10)·3

             4x + 60 &#8804; 12x - 30

                  4x &#8804; 12x - 90

                 -8x &#8804; -90

We divide both sides by -8.  But when we multiply or 
divide both sides of an inequality by a negative number, 
the inequality symbol is reversed:

                 {{{(-8x)/(-8)}}} &#8805; {{{(-90)/(-8)}}}

                   x &#8805; {{{45/4}}}

                   x &#8805; 11.25  

To write the solution set in set-builder notation:

                 {x | x &#8805; 11.25}


------------------------------------------------------


                 {{{-7/8}}}x &#8805; {{{-3/16}}} 
 
Clear both fractions by multiplying both sides by -16.
But when we multiply or divide both sides of an inequality 
by a negative number, the inequality symbol is reversed:

       (-16)·{{{-7/8}}}x &#8805; (-16)·{{{-3/16}}}
                     14x &#8804; 3

Divide both sides by 14.
(The  > symbol does not reverse when we multiply
or divide both sides by a positive number)
  
                     {{{14x/14}}} &#8804; {{{3/14}}}
                       x &#8804; {{{3/14}}}    

To write the solution set in set-builder notation:


                     {x | x &#8804; {{{3/14}}}}

Edwin</pre>