How do i find the solution set? 
6(r-9)+3 > 7(r+3)-22


Solve it just like an equation with one exception:


6(r - 9) + 3 > 7(r + 3) - 22

 6r - 54 + 3 > 7r + 21 - 22

     6r - 51 > 7r - 1

     6r - 7r > 51 - 1

         -1r > 50

Up to here the proble is exactly the same as if there
had been an " = " instead of a " > "

Her is where it is different.  When you divide (or multiply)
an inequality by a negative number, you must change the 
direction of the inequality. 

We need to divide both sides by -1, the coefficient of r, so we must
change the " > " to " < "
 
-1r    50
——— < ————
-1     -1

  r < -50

You can either express this in set builder notation as

{r|r is real and r < -50}

or in interval notation as  (-oo, -50)

Edwin
AnlytcPhil@aol.com