I used the test-point method, but you could also use the sign graph of
factors method.

This quadratic inequality is already in standard form.

Below is a graph that marks off the boundary points -7
and 2 and shows
the three sections that those points have created on the graph.
Note
that open holes were used on those two points since our original
inequality
did not include where it is equal to 0 and 2 makes the denominator
0.

Note that the two boundary points create three sections on the graph: , , and .

You can choose ANY point in an interval to represent
that interval.
Remember that we are not interested in the actual value that we get,
but
what SIGN (positive or negative) that we get.

Keep in mind that our original problem is .
Since we are looking for the quadratic expression to be **LESS
THAN 0**, that means we need our sign to be **NEGATIVE**.

**From the interval ,
I choose to use -8 to test this interval:**

(I could have used -10, -25, or -10000 as long as it is in the interval)

(I could have used -6, -5, or -4 as long as it is in the interval)

***Chose 0 from 2nd interval to
plug in for x **

(I could have used 10, 25, or 10000 as long as it is in the interval)

**Graph: **

***Visual showing all numbers
between -7 and
2 on the number line**

I used the test-point method, but you could also use the sign graph of
factors method.

***Inv. of add. 2 is sub. 2**

***Rewrite 2nd fraction with LCD
of x - 2**

Below is a graph that marks off the boundary points -5
and 2 and shows
the three sections that those points have created on the graph.
Note
that there is an open hole at -2. Since that is the value that
cause
the denominator to be 0, we cannot include where *x* = 2. Since our inequality includes where it is equal to 0, and -5
causes only the numerator to be 0 there is a closed hole at -5.

Note that the two boundary points create three sections on the graph: , , and .

You can choose ANY point in an interval to represent
that interval.
Remember that we are not interested in the actual value that we get,
but
what SIGN (positive or negative) that we get.

Keep in mind that our inequality is __>__ 0. Since we are looking for the quadratic expression to be **GREATER
THAN OR EQUAL TO 0**, that means we need our sign to be **POSITIVE
(OR O)**.

**From the interval ,
I choose to use -6 to test this interval:**

(I could have used -10, -25, or -10000 as long as it is in the interval)

(I could have used -4, -3, or -2 as long as it is in the interval)

(I could have used 10, 25, or 10000 as long as it is in the interval)

**Graph: **

***Visual showing all numbers
less than or equal
to -5 and indicating all values greater then 2**

Last revised on Jan. 2, 2010 by Kim Seward.

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