Download Document

Bell Work
The World Travelers Club is selling chips to raise money
to go to Australia. It costs $4500 in total. Ulises
receives $300 from a rich old man as a donation.
If he charges $1.50 for each bag of chips, how many
does he need to sell in order to raise at least enough
for his trip?
1. Write an inequality
2. Solve it
Bell Work
What is this a picture of?
Bell Work
THE SHOWDOWN
Get in your groups of 4
1 Showdown Captain
3 students with whiteboards
Compound inequalities
A compound inequality are two inequalities
connected by the words “and” or “or”.
For example:
2<x<6
1
2
3
4
5
6
7
8
9
At the Golden Corral, an individual
must be between 3 years AND 12
years old to pay the child's price.
3
12
In order to get a flu shot for free
you have to be less than or equal
to 5 years old OR 65 years or
older.
5
65
Graphing “AND”
0<x<4
-2
-1
0
1
2
3
4
5
6
“AND” cases have the variable in-between
two numbers. The graph is in-between two
numbers.
Graphing “OR”
-2
-1
0
1
2
3
4
5
6
x < -1 or x > 2
OR cases have TWO separate answers and
are solved (and graphed) separately (but on
the same number line).
AND or OR
Solving “AND”
SOLVE: Isolate the variable in-between the
inequality symbols.
IMPORTANT – opposite operations apply to the
WHOLE THING (that means both sides!).
-2 <x – 8 < 10
-2 + 8 < x – 8 + 8 < 10 + 8
6 < x < 18
Original Problem
Add 8
Simplify
I DO
Solve 4 < x – 5 < 12. Graph the solution.
YOU TRY!
Solve -9 < 3x + 6 < 10. Graph the solution.
Solving “OR”
SOLVE: You MUST solve AND graph each
inequality separately (but on the same number
line).
Solve:
3x + 1 < 7 OR 11x – 4 > 62
YOU TRY!
Solve Separately, Graph Together
3 + p >14
OR
-2p + 6 > 30
Multiplying or Dividing by
negative numbers
AND Inequality
Reverse BOTH signs
-2 < -x < 5
2 > x > -5
Multiplying or Dividing by
negative numbers
“OR” inequalities
only reverse it if it applies to the
individual inequality.
-3x + 1 < 7 OR 11x – 4 > 62
YOU TRY!
Solve
-2 < -2 – x < 1
Compound Inequalities
When graphing compound inequalities, be sure that
the graph satisfies BOTH if it is AND or ONE if it is
OR…….inequality.
-3 > x OR x > 2
-5
-4
-3
-2
-1
0
1
2
3
Write an inequality that describes each
condition.
a. Water is a nonliquid when the temperature is 32 degrees F
or below, or is at least 212 degrees F.
b. A refrigerator is designed to work on an electric line
carrying from 115 to 120 volts.
Quick Review
Solve inequalities just as you would equations using inverse
operations, KNOW WHEN AND WHEN NOT TO FLIP
INEQUALITY SIGNS!!!
Make sure your graph agrees with the inequalities involved.
What does the graph of a compound inequality (AND) case
look like? OR Case?
Homework
P208, 16-26 even, 30-34 even, 47-50