MS112 Worksheet
Dr. Y. Kim
6.6 Quadratic Inequalities
Recall:
open interval
closed interval
Remember Solutions to equations a number/ numbers
Solutions to inequalities an interval/ union of intervals
Ex1) Solve 013
>
+
x and write the solution in interval notation.
Graph the solution.
*Ex2) Solve
082
2
>−− xx for
x
. Write the answer in the interval form.
step1.
Factor the left side. (Make sure 0 in the right side)
step2.
Find the key numbers(= the solution to the equation)
step3.
Mark the key numbers on a real line.
step4.
Check each interval using a test number.
step5.
Check the boundary points(=the key numbers)
Ex3) Solve for
x
.
1.
0)3)(1(
≤
−
−
xx
2.
0)32)(23(
>
−
+
xx
Inequality Notation
Interval Notation
52
<
<
x
(
)
5,2
52
≤
≤
x
[
]
5,2
52
<
≤
x
[
)
5,2
52
≤
<
x
(
]
5,2
5
<
x
(
)
5,∞
x
<
2
(
)
∞,2
