9x - 2x > 14 - 9(-x - 4)

Solve it exactly as you would an equation, that is,
if the " < " had been an " = ", until you get to 
the last step:

9x - 2x > 14 - 9(-x - 4)
     7x > 14 + 9x + 36
     7x > 50 + 9x
    -2x > 50

Now at this last step where you divide both sides by the
coefficient -2, there are two rules you must remember
that you don't have to remember when solving equations.

1.  If you divide both sides by a POSITIVE number, LEAVE
    the symbol of inequality as it is.
2.  If you divide both sides by a NEGATIVE number, REVERSE
    the symbol of inequality.

In this case we divide both sides by a NEGATIVE number,
namely -2.  Therefore we must use rule 2 and REVERSE the
symbol > to <.

    -2x       50
   -----  <  ----
     -2       -2

        x < -25

The graph of that looks like this

 <========o----------   
         -25  

In interval notation this is abbreviated to 
(-infinity, -25)

Edwin