September 22, 2011
Warm ups 2-4
Solve
1. 3- 8 | x - 4 | ≥ -21
2. | 2x - 5 | ≥ 4
3. | 5x + 1| ≤ -6
September 22, 2011
INEQUALITIES can be tricky!
1. x2 < 16
check!
2. x2 + 1 > 26
3. 3x2-11x-4<0
September 22, 2011
This is called factoring and stating cases
We could have instead used the graphing
method.
3x2 - 11x - 4 < 0
Thi
s is
September 22, 2011
Solve x2 - 6x > -8 using both methods
September 22, 2011
A third method involves using CRITICAL POINTS.
Solve the previous problems with this method
1. 3x2 - 11x - 4 < 0
3. x2 < 16
2. x2 - 6x > -8
September 22, 2011
The factoring and stating cases method is best for simple
quadratic cases (and for understanding), but the critical points
method works better on higher order inequalities, and the
graphing method works best on more complicated inequalities.
Solve:
1. x3-x2-6x > 0
2. |x| < 2 - x2 + 2x
3.
September 22, 2011
For what value(s) of k is x2 +3kx - k > 0
true for all values of x?
What if it had been ≥ ?
September 22, 2011
#2-4 p. 54 1 LC, 2 LC, 3, 5, 6, 8
September 22, 2011