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Chapter 22-1 Graphing Inequalities
ObjectivesThe students will learn to:Identify solutions of inequalities in one
variableWrite and graph inequalities in one variable
What is an inequality ?An inequality is a statement that two
quantities are not equal. The quantities are compared by using the following signs:
≤A ≤ B
A is less than or
equal to B.
<A < B
A is lessthan B.
>A > B
A is greaterthan B.
≥A ≥ B
A is greaterthan or
equal to B.
≠A ≠ B
A is notequal to B.
What is a solution to an Inequality?Answer: A solution of an inequality is any value of
the variable that makes the inequality true.
Identifying Solutions of inequalitiesExample #1Describe the solutions of x – 6 ≥ 4 in
wordsx -3 0 9.9 10 10.1 12
X-6 -9 -6 3.9 4 4.1 6
x – 6 ≥ 4
–9 ≥ 4
–6 ≥ 4
3.9 ≥ 4
4 ≥ 4 4.1 ≥ 4
6 ≥ 4
Solution?
No NO NO Yes Yes Yes
Example #1 solutionWhen the value of x is a number less than
10, the value of x – 6 is less than 4. When the value of x is 10, the value of x –
6 is equal to 4.When the value of x is a number greater
than 10, the value of x – 6 is greater than 4.
Solution:It appears that the solutions of x – 6 ≥ 4 are all real numbers greater than or equal to 10.
Example #2Describe the solutions of 2p > 8 in words.
p -3 0 3.9 4 4.1 5
2p -6 0 7.8 8 8.2 10
2p > 8
-6 > 8
0 > 8 7.8 > 8
8 > 8 8.2 > 8
10 > 8
Solution?
No NO NO No Yes Yes
Example #2 solutionWhen the value of p is a number less than
4, the value of 2p is less than 8. When the value of p is 4, the value of 2p is
equal to 8.When the value of p is a number greater
than 4, the value of 2p is greater than 8.Solution: It appears that the solutions of 2p
> 8 are all real numbers greater than 4.
How to graph linear inequalities?How can we graph an inequality like 3 + x < 9 An inequality like 3 + x < 9 has too many
solutions to list. You can use a graph on a number line to show all the solutions.
Solution:
Graph Inequality Graph x > 2Solution:Draw a non-shaded or open circle at 2 and
shade everything on the right of 2. The shaded area in red is your solution. It means that the solution can be any number on the right of 2.Notice that 2 is not shaded because 2 is not included in your solution.
Graph inequalitiesGraph x ≥ 6
Solution:Draw a shaded circle at 6 and then shade everything on the right of 6Notice that this time, the circle is shaded because x is also equal to 6.
Graph inequalitiesGraph x ≤ -1Solution:Draw a shaded circle at -1 and then shade
everything on the left of -1
Graph inequalities22 – 4 ≥ w m ≤ –3
Student Guided practiceWork on problems 1-10 from worksheet
Writing Linear inequalitiesWrite the inequality shown by each graph.
Solution: x < 2
Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2 means that 2 is not a solution, so use <.
Writing linear inequalitiesWrite the inequality shown by each graph.
Student guided practiceGo over writing linear inequalities worksheet problems 3-10
Graphing linear inequalities applicationsRay’s dad told him not to turn on the air
conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions.
Solution: t 85
75 80 85 9070
Application’s example A store’s employees earn at least $8.50
per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.
HomeworkDo problems 22-31 from page 103
ClosureToday we saw about graphing and writing
linear inequalities Next class we are going to learn how to solve
for them
Have a great day!!