Get 0 on the right:
Get LCD
The critical values are when the numerator or
the denominator equals 0:
The numerator is 0 when x = 3
The denominator is 0 when x = 2
So we draw a number line and mark the critical
numbers
-----------------o---o- ---------
-2 -1 0 1 2 3 4 5 6
This divides the number line into three intervals
We pick a test value in the left-most interval.
The easiest number there to pick for a test value
is 0, so we substitute it in the inequality:
That's false so we do not shade the numbers in the
left most region, so we still have
-----------------o---o-----------
-2 -1 0 1 2 3 4 5 6
We pick a test value in the middle interval, between
2 and 3. The easiest number there to pick for a test value
is 2.5, so we substitute it in the inequality:
That's true so we shade the numbers in the
middle region, so we now have
-----------------o===o----------
-2 -1 0 1 2 3 4 5 6
We pick a test value in the right-most interval, greater
than 3. The easiest number there to pick for a test value
is 4, so we substitute it in the inequality:
That's false so we do not shade the numbers in the
right-most region, so we have
-----------------o===o-----------
-2 -1 0 1 2 3 4 5 6
Finally we test the critical numbers themselves:
We test 2
1/0 is not defined, so we do not shade at 2
We test 3
That's true so we do shade at 3
-----------------o===☻-----------
-2 -1 0 1 2 3 4 5 6
Interval notation:
Edwin
