(x+5)(x-9)(x+3) > 0
The critical numbers are numbers which when substituted for x
causes the left side either equal to 0 or undefined.
These critical numbers are -5, 9, and -3
Mark those with open circles on the number line:
----------o-----o-----------------------------------o------------
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
We choose a number less than -5, say -6, and substitute it in the
inequality:
(x+5)(x-9)(x+3) > 0
(-6+5)(-6-9)(-6+3) > 0
(-1)(-15)(-3) > 0
-45 > 0
That's false, so we do not shade the number line left of -5
We choose a number between -5 and -3, say -4, and substitute it in the
inequality:
(x+5)(x-9)(x+3) > 0
(-4+5)(-4-9)(-4+3) > 0
(1)(-13)(-1) > 0
13 > 0
That's true, so we do shade the number line between -5 and -3:
----------o=====o-----------------------------------o------------
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
We choose a number between -3 and 9, say 0, and substitute it in the
inequality:
(x+5)(x-9)(x+3) > 0
(0+5)(0-9)(0+3) > 0
(5)(-9)(3) > 0
-135 > 0
That's false, so we do not shade the number line between -3 and 9:
We choose a number greater than 9, say 10, and substitute it in the
inequality:
(x+5)(x-9)(x+3) > 0
(10+5)(10-9)(10+3) > 0
(15)(1)(13) > 0
195 > 0
That's true, so we do shade the number line right of 9
----------o=====o-----------------------------------o============>
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Answer: {x| -5 < x < -3 OR x > 9 }
Edwin
