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Friday!!!!
• Review your homework with
your partner.
• Be ready to ask questions!!!
Silent Auction
• What is a Silent Auction?
• Bids are not known!
• Bidders unknown by others!!
• Eliminates Peer Pressure?
Silent Auction: Question?
• How many did not check your answers on
the website??
FRIDAY
Check It Out!!
Answers!!
1. 6
2. 21
3. All Real Numbers
4. 16/17 or .94
5. 2
6. 13/12 or 1.1
7. No Solution
8. -8/3 or -2.7
9. 48
10. -15
11. 29/3 or 9.67
12. 4
13. 25(7.75) + 6.25x = 250
x = 9 hours
14. 425.14 + 45x = 824.14
x = 8.87 hours
Supplies
• You will need the dry
erase markers for our
class work!!
Unit 1
Solving
Inequalities
Objectives
• I can write a solution in
Inequality Notation and
Interval Notation
• I can solve and graph
inequalities with one
variable
Number Line
What number?
 Infinity 
What number?
Graphing the Inequalities
• An open circle indicates the number is
excluded from the solution
• A closed circle indicates the number is
included in the solution
• Draw a number line with at least 3 numbers,
plus the direction arrow.
• Lets do some examples
Open Circles
• Used when you have the inequality symbols
(< or >).
• The open circle means the number being
circles is not in the solution.
• x>2
• Graph:
1
2
3
Closed Circles
• Closed Circles used when the inequalities
are ( or ).
• Closed circles mean the number being
circles is in the solution set.
• x2
• Graph:
1
2
3
EXAMPLE 1
Graph simple inequalities
a. Graph x < 2.
The solutions are all real numbers less than 2.
An open dot is used in the graph to indicate 2 is not
a solution.
EXAMPLE 1
Graph simple inequalities
b. Graph x ≥ – 1.
The solutions are all real numbers greater than or
equal to – 1.
A solid dot is used in the graph to indicate – 1 is a
solution.
EXAMPLE 2
Graph compound inequalities
a. Graph – 1 < x < 2.
The solutions are all real numbers that are greater
than – 1 and less than 2.
EXAMPLE 2
Graph compound inequalities
b. Graph x ≤ – 2 or x > 1.
The solutions are all real numbers that are less than or
equal to – 2 or greater than 1.
How many of you have a “nickname” or
another name that you are called by?
x≥2
Inequality (Set) Notation (INQ)
         








 
[2, ) Interval Notation (INT)
x2
x  3
3  x  8
These are in Inequality Notation
(Set Notation)
We are going to change them
to INTERVAL NOTATION
What is Interval Notation?
[ ]
means “included” (equal
to)
Like a closed dot,
( )
, > <
means “not included”
Like an open dot,
, > <
HIGHLIGHT THIS IN YOUR NOTEBOOK!


Infinity???
All negative numbers
All positive numbers
We ALWAYS use ( ) with
infinity!!!
HIGHLIGHT THIS IN YOUR NOTEBOOK!
Symbols
• INQ: Inequality Notation
• INT: Interval Notation
INQ
x4
Num Line
INT
( , 4)
INQ
x2
Num Line
INT
(2, )
INQ
x 1
Num Line
INT
( ,1]
INQ
2  x  4
Num Line
INT
(2, 4]
INQ
3  x  2
Num Line
INT
(3, 2)
INQ x  7
or
x  11
Num Line
INT (, 7) U [11, )
What would be different for these
in Interval Notation?
[3, 2]
[3, 2)
(3, 2)
PRACTICE
x 8
Graph it on a number line.
Change it to interval notation
PRACTICE
x  5
Graph it on a number line.
Change it to interval notation
PRACTICE
3  x  8
Graph it on a number line.
Change it to interval notation
PRACTICE
x  3 or
x6
Graph it on a number line.
Change it to interval notation
What would we do if the
solution was ALL REAL
NUMBERS?
         
Interval
Notation?
Inequality
Notation?








 
(,)

Practice
• Complete page 1 of WS 1-2 with your
partner.
Solving Inequalities
ALMOST the same as solving equations!
1. Get the variable terms together on the left
side of the equation
2. Move all the numbers to the other side of
the equation.
3. DIVISION is the LAST step
Ex 1: 6x + 3 > 5x -2
• 6x + 3 > 5x –2
• x + 3 > -2 (subtracted 5x from both sides)
• x > -5 (subtracted 3 from both sides)
BIG DIFFERENCE
If you multiply or divide each side
of an inequality by a negative
number then the order of the
inequality must be switched.
Ex 2: 3 + 2x < 3x + 9
•
•
•
•
3 + 2x < 3x + 9
3 – x < 9 (subtracted 3x from both sides)
-x < 6 ( subtracted 3 from both sides)
x > -6 (divided both sides by –1, switched
the inequality sign)
• x > -6
EXAMPLE 4
Solve an inequality with a variable on both sides
Solve 5x + 2 > 7x – 4. Then graph the solution.
5x + 2 > 7x – 4
– 2x + 2 > – 4
– 2x > – 6
x<3
Write original inequality.
Subtract 7x from each side.
Subtract 2 from each side.
Divide each side by – 2 and reverse the
inequality.
ANSWER
The solutions are all real numbers less than 3. The
graph is shown below.
Word Problems
You have $500 to replace your
bathroom floor tile. The tile cost $370
and the tile saw costs $40 per hour to
rent. Write and solve an inequality to
find the possible numbers of hours
you can rent the saw and stay under
your budget.
Solution:
• Total money: $500
• Tile: $370
• Saw Rental: $40 per hour
• Possible Inequality:
• 370 + 40x ≤ 500
• x ≤ 3.25 hours
Homework
• WS 1-2 Inequalities
• Keep working on Projects