Transcript pc2-5-Inequalities

Inequalities
Lesson 2.5
Interval Notation
Let c and d be real numbers with c < d
 c, d  means c  x  d{closed }
 c, d  means c  x  d {open}
[c, d ) means c  x  d {half  open}
(c, d ] means c  x  d {half  open}
Lets contemplate infinity!
Solving Inequalities – graph this as
well!
solve :2  3 x  5  2 x  11
What happens when the last thing
you do to isolate a variable is to
multiply or divide by a negative
number?
Some Other Tidbits! – pg. 121
The solutions of an inequality of the
form f(x) < g(x) consist of intervals on
the x-axis where the graph of “f” is
below the graph of “g”.
The solutions of f(x) > g(x) consist of
intervals on the x-axis where the
graph of f is above the graph of g.
The graph of y = f(x) – g(x) lies above
the x-axis when f(x) – g(x) > 0 and
below the x-axis when f(x) – g(x) < 0.
Solving an Inequality….again?
x  10 x  21x  40 x  80
4
3
2
rewrite as x  10 x  21x  (40 x  80)  0
4
3
2
Solving Quadratic Inequality
2x2 + 3x – 4 ≤ 0 {on page 122}
In fact, let’s take a little gander shall
we?
One more example
x  x2

0
2
x  2x  3
2