5 - 9x > 19 + 5x 

subtract 5 from both sides

          -9x > 14 + 5x

Subtract 5x from both sides

         -14x > 14

Divide both sides by -14, remembering the rules:

1. When dividing or multiplying both sides of an inequality through by a
NEGATIVE number, REVERSE the direction of the inequality.
2. When dividing or multiplying both sides of an inequality through by a
POSITIVE number, KEEP, DO NOT REVERSE, the direction of the inequality.

Since -14 is negative, Rule 1 applies, so we REVERSE the direction of the
inequality from > to <

           x < -1

In set builder notation the solution set is written 

         {x | x < -1}

In interval notation the solution set is written

            (oo, -1]

Edwin
AnlytcPhil@aol.com