Writing

1
Writing Graphing Inequalities

• Learning Target Today I am learning how to
  write and graph inequalities on the number line
  because I want to be able to represent situations
  that have more than one correct answer.

2
Where might I see inequalities in real life?
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6

• If its any smaller, youve got to throw him back!

7
Opening

1. You are going to Six Flags as soon as school is
   out (yaay!). You have to be at least 4 ft. tall
   to ride some of your favorite rides, but it isnt
   only 4-foot tall people who can ride the rides!
   How tall can you be and ride the rides?
2. See if you can figure out how to represent this
   with an inequality sign and a variable. (Hint
   if it were an equation it would look like this x
   4 ft. Use one of the inequality symbols posted
   on the board to make it an inequality.)
3. What are the possible solutions for x (the
   variable)?

4 ft. tall and taller
x gt 4 ft.
4, 41, 42 . . . 6, 61, etc.! And
everything in between!
8

• What are some other situations that have more
  than one answer or qualifying response?

Examples Scores that qualify for an A gt
90 Money you need to get into Six Flags gt
39 Age required to get the kids meal lt
10 years old) Number of days to complete
your project lt 5 days
9
Writing and Graphing Inequalities

• Dr. Burger helps us write inequalities

10
An inequality states that two quantities either
are not equal or may not be equal. An inequality
uses one of the following symbols
Symbol Meaning Word Phrases
lt
gt


Fewer than, below
is less than
is greater than
More than, above
is less than or equal to
At most, no more than
is greater than or equal to
At least, no less than
11

• And

Symbol Meaning Word Phrases
?
is not equal to
Is not equal to
12

• An inequality that contains a variable is an
  algebraic inequality. A value of the variable
  that makes the inequality true is a solution of
  the inequality.

An inequality may have more than one solution.
Together, all of the solutions are called the
solution set.
13
Write an inequality for each situation.
A. There are at least 15 people in the waiting
room.
At least means greater than or equal to.
number of people 15 or x 15
B. The tram attendant will allow no more
than 60 people on the tram.
No more than means less than or equal to.
number of people 60 or x 60
14
Check It Out Example 1
Write an inequality for each situation.
C. There are at most 10 gallons of gas in the
tank.
At most means less than or equal to.
gallons of gas 10 or x 10
D. There are at least 10 yards of fabric left.
At least means greater than or equal to.
yards of fabric 10 or x 10
15

• Write about what youve learned
• Complete Reading Strategies
• Use complete sentences.
• Turn it over on your desk when done. It will be
  collected.
• Make sure your name, date, class period are on
  it!

16
Graphing Inequalities

• Words arent enough. I want to show an
  inequality on a number line. Can I do that??
• Dr. Burger says yes! We can graph inequalities

17
You can graph the solutions of an inequality on a
number line. If the variable is greater than or
less than a number, then that number is
indicated with an open circle.
To indicate that solutions include numbers with
values less than the point graphed, shade to the
left of the point.
To show that solutions include numbers greater
than the point graphed, shade to the right of the
point.
18
This open circle shows that 5 is not a solution.
a gt 5
If the variable is greater than or equal to or
less than or equal to a number, that number is
indicated with a closed circle.
This closed circle shows that 3 is a solution.
b 3
19
Symbols Review

• Open Circle

• Closed Circle

• The number is not included in the solution.

• The number is included in the solution.

20
Additional Example 2 Graphing Simple Inequalities
On your own paper, graph each inequality.
A. n lt 3
3 is not a solution, so draw an open circle at
3. Shade the line to the left of 3.
2 1 0 1 2 3
B. a 4
4 is a solution, so draw a closed circle at 4.
Shade the line to the right of 4.
6 4 2 0 2 4 6
21
Check It Out Example 2
On your own paper, graph each inequality.
A. p 2
2 is a solution, so draw a closed circle at 2.
Shade the line to the left of 2.
3 2 1 0 1 2 3
B. e gt 2
2 is not a solution, so draw an open circle at
2. Shade the line to the right of 2.
3 2 1 0 1 2 3
22
Insert Lesson Title Here
Lesson Quiz Part II
Graph the inequalities on your own paper. 1. x
gt 1
2. x lt 1
23
Insert Lesson Title Here
Lesson Quiz Part II
Graph the inequalities, continued. 3. x gt 1
4. x lt 1
24
Now lets make our own review flip books!
25
Lets begin by taking the 3 pieces of paper you
were given and stacking them with about a 1-2
inch overlap
26
Now hold the papers together and fold the top
down so you have six 1-2 inch flaps, and put two
staples at the very top to hold your flip book
together.
27
Write Inequalities on the top flap
28
Copy the following graphs onto each new flap on
your flip book as they are shown to you. Make
sure that you pay attention whether the circles
are open or closed!
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
Now that weve completed the graphs for our flip
books, lets begin writing the inequalities that
each graph represents. Make sure that you can
write the inequality with the variable both on
the right AND the left of the inequality sign.
What happens when you switch the side that the
inequality is on?
34
Now go through each graph and fill in the
inequalities. When you have finished, check with
a partner close to you.
35
How did you do?! Temperature Check!
Give me a thumbs up if you did a great job and
didnt miss any
Give me a sideways thumb if you did alright, but
you probably need to work on it a little bit
Give me a thumbs down if you arent getting it
yet, and you need some help
36
Lets get wordy!
Who remembers some key words and phrases that
tell us which inequality sign to choose? Raise
your hand!
37
Now we will use these key words to write some
word problems for our inequality graphs. Look at
the example below to see what I mean
38
Are you pickin up what Im puttin down?
39
Lets finish up by writing word problems for the
rest of the graphs. Try to do them on your own,
and have your elbow partner check when youve
finished.