Get 0 on the right:
Write as
Get the LCD of (x+2) and
multiply top and bottom of
by that:
Combine the numerators over the LCD:
Remove the parentheses in the top:
Combine like terms:
Find the critical values by setting both
the numerator and the denominator equal to
zereo and solving:
gives critical value gives critical value
Indicate the critical values on a number line:
-------------o-------------------o------------------------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
Choose a number left of -7, say -8.
Substitute it into the original or the factored form.
It's easier to use the factored form:
That is false so we do not shade the part
to the left of . We still have the
number line
-------------o-------------------o------------------------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
Choose a number between -7 and -2, say -3.
Substitute it into the original or the factored form.
It's easier to use the factored form:
That is true so we do shade the part between
and .
-------------o===================o------------------------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
Choose a number right of -2, say 0.
Substitute it into the original or the factored form.
It's easier to use the factored form:
That is false so we do not shade the part
to the right of . We end up with the
number line
-------------o===================o------------------------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
We need only test the endpoints of the interval when the
symbol of inequality is < or >.
The answer in interval notation is (-7,-2).
Edwin
