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
