Question 30554
<pre><b><font size = 3>       5 - 9x <u>></u> 19 + 5x 

subtract 5 from both sides

          -9x <u>></u> 14 + 5x

Subtract 5x from both sides

         -14x <u>></u> 14

Divide both sides by -14, remembering the rules:

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

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

           x <u><</u> -1

In set builder notation the solution set is written 

         {x | x <u><</u> -1}

In interval notation the solution set is written

            (oo, -1]

Edwin
AnlytcPhil@aol.com</pre>