Algebra 1
Unit 7, Lesson 1: Graphing Inequalities in One Variable
Objectives
Unit
Skills
-
Students will be able to graph inequalities in the form x >
a, x < a, a < x, a > x
- Students will be able to graph compound inequalities
- Students will be able to write an inequality, given its
number line graph
Materials and Handouts
Homework
- Do Now handout
#7-1: Graphing
- Guided practice packet and keynote
Inequalities &
- Practice handouts
Solving Systems
- Homework #7-1
Time
15 min
45 min
20 min
Activity
Do Now: Comparing Numbers
- Students compare numbers and expressions
- Review the number line definition of greater than / less than:
with any two numbers, the one on the left on the number line is
the lesser.
- So, if we say x < -5, what are some numbers that can take the
place of x? What are some numbers that come to the left of -5
on the number line?
Guided Practice
- Take students through the packet that introduces inequalities.
Work through the examples and then have them do the practice
problems.
- Call students to the board to present answers to practice
problems in each section.
- In the middle, there is a think-pair-share section. Students
should summarize what they have been doing silently for about 2
minutes, and then explain their answer to their partner. Call
on a few people to read their summaries to the class.
- For part 5, one method that might help is to have students label
the end points with their values, and write “x” above the arrow.
Then think, is the x to the right or left of the end point. Use
this to determine which inequality symbol should be there.
Individual Practice (if there is time)
- Students work independently on practice problems. Also includes
a system of equations in standard form, as this will be on the
next skills tests.
Algebra 1
Unit 4 Inequalites
Period:
Name:
Comparing Numbers
<
“Less than” means “is to the left of” on the
number line
>
“Greater than” means “is to the right of” on
the number line
Directions: Put the correct inequality symbol (either < or > )
between each pair of numbers. Use the number line and the
information in the box to help you.
Example:
-4.
-7
< -4 because, on the number line, -7 is to the left of
-5
-3
10
0
-5
-4
8
-8
-5
-10
0
3.5
3.1
12
-9
1
-14
-15
-6.8
-8.6
-10.4
-4.1
0
9.75
Directions: Write each set of numbers in order from least to
greatest.
______
-6
10
-8
______ ______
5
0
______
-3
______
______
______
______
-9
-10
-3
______ ______
-8
3.7
-5.2
8½
0
______ ______ ______
-11
-2.9
5
______
-3.4
______
______
______
______
Algebra 1
Period:
Unit 4 Inequalities: Lecture Notes/CW
Name:
Main Concept
Part 1: Why is that little line so important?
the same as < )
( < is not
Together
1.
List four solutions to the inequality x < 6.
x = ______
______
or
x = ______
or
x = ______
or
x =
List three solutions to the inequality x < 6 that are greater than 5.
x = ______
or
Is x = 6 a solution?
x = ______
or
x = ______
Why or why not?
Plot all of the solutions we listed on the number line below.
How many more solutions are there?
below.
How can we plot them all?
How can we deal with the endpoint at 6?
Let’s do that
Let’s finish the graph.
2.
What is the difference between x < 2 and x < 2?
Graph all the solutions of x < 2.
What should the endpoint look like?
Graph all the solutions of x < 2.
What should the endpoint look like?
Graph all the solutions of x > -5.
What should the endpoint look like?
You Practice
Make a graph of each inequality.
Pay attention to the endpoints.
x < 10
x < -9
x > 0
x > 7
(sketch a graph)
Part 2: Which side is the x written on?
Together
List four solutions to the inequality 3 < x.
the _______ of x on the number line.
x = ______
______
or
x = ______
or
In this situation, 3 is to
x = ______
or
x =
Plot all of the solutions we listed on the number line below.
Which direction will we draw the arrow?
Let’s finish the graph.
This is the same graph as the inequality __________.
We can move the x to
the left side of the inequality as long as we flip this inequality symbol.
You Practice
Make a graph of each inequality.
the x is.
Pay attention to the endpoints and where
8 > x
Rewrite with x on the left: ___________
-2 < x
Rewrite with x on the left: ___________
6.5 < x
Rewrite with x on the left: ___________
-7.9 < x Rewrite with x on the left: ___________
(sketch a graph)
Part 3: Think-Pair-Share
Prompt: In your own words, how do you make a graph of an inequality?
do you have to watch out for?
What
Part 4: Compound Inequalities (more than one inequality)
1. “Or” Inequalities
Together
Plot all of the solutions to the inequality x < -2 or x > 4 on the number
line below.
You Practice
Make a graph of each “or” inequality.
x < 2 or x > 6
-3 > x or x > 0
x < -7 or -1 < x
x < -6 or x > 6
(sketch a graph)
2. “Between” Inequalities
Together
List six solutions to the inequality -2 < x < 7.
x = ______
or
or
x = ______
or
x = ______
or
x = ______
x = ______
or
x = ______
Plot these solutions on the number line.
What do the endpoints look like?
Let’s make the final graph below:
We can say that “x is _______________ -2 and 7”.
You Practice
Make a graph of each “between” inequality.
3 < x < 8
-10 < x < -4
-8 < x < 0
-5 < x < 9
(sketch a graph)
Part 5: Writing Inequalities
Together
Write the inequality that each graph represents.
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
7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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You Practice
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7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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7
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1
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Algebra 1
Unit 4 Inequalities: HW
Period:
Name:
Graphing Inequalities
Part 1:
Sketch a number line graph of each inequality
x < -4
x > 8
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
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
7
5 < x
6
5
4
3
2
1
0
1
2
3
4
5
6
7
-3 > x
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
7
6
5
4
3
2
1
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7
7
x < -5 or x > -1
6
5
4
3
2
1
0
1
2
3
4
5
6
7
2 > x or 5.5 < x
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
7
6
5
4
3
2
1
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7
7
-7 < x < 10
6
5
4
3
2
1
0
1
2
3
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5
6
7
0 < x < 5
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
7
6
5
4
3
2
1
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7
7
3.5 < x < 6¼
6
5
4
3
2
1
0
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2
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7
-3 < x < 5 or x > 7
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
7
6
5
Part 2:
4
3
2
1
0
1
2
3
4
5
6
7
7
6
5
4
3
2
1
0
1
2
3
4
Write the inequality that is represented by each number line graph
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
7
6
5
4
3
2
1
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7
6
5
4
3
2
1
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7
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Part 3:
Write an inequality for each example below.
Phrase
13.
Be sure to drink at
least 6 glasses of water
a day
14.
A jello cup has fewer
than 120 calories
15.
Don’t spend more than
ten dollars.
Translation
The number of glasses is
greater than or equal to
6
16.
Students at Rex Putnam
are between 14 and 19
years old.
The youngest student at
Rex Putnam is 14, the
oldest is 19.
Inequality
The number of calories
is less than 120
The amount you can spend
is 10 dollars or less
Part 4: Solve for the unknown (this is review- next class we will be
“Solving Inequalities”)
17.
 8  p  13
18.
418  22a
19.
29  3n  13

20.
21 
x
18
21.
3 p  2  29
22.
x
14  25
6

23.
1  r  5
26.
2(x - 3) = 5x + 12
24.
 5x  13  17
25.
m  13
 8
2
Algebra 1
Homework #7-1
Period:
Name:
Graphing Inequalities & Solving
Systems
Part 1:
Sketch a number line graph of each inequality
x > -3
x < 9
-6 < x
7.5 > x
x < 0 or x > 5
-4 > x or 4 < x
-8 < x < 2
6.5 < x < 15
0 < x < 7¾
x < -7 or -2 < x < 3
Part 2:
Write the inequality that is represented by each number line graph
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
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
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
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
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
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
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
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
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
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
Do the problem on
back!
Part 3: Solve the system of equations with algebra and by graphing.
3x  4y  20

2x  y  6
Algebra Method
(Elimination)
Graph Method
(Change each to y = mx + b and then see where the lines cross)
QuickTime™ and a
decompressor
are needed to see this picture.