Inequalities and Their Graphs

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Inequalities and Their Graphs
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Inequalities What do they mean in words?

• Less than or smaller than
• Fewer than

• Less than or equal to
• At most

• No more than
• A maximum of

• Greater than or bigger than
• More than

• Greater than or equal to
• At least

• No less than
• A minimum of

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Example
Write an inequality to describe people who are
NOT of legal driving age in California
First- try to put it in words
Who are the people who can not drive?
Everyone younger than or less than 16 years old
people who cant drive are less than 16
plt16
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When we start graphing we have to remember
Use OPEN bullet for
Use CLOSED bullet for
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• Graph X -1
• Graph K gt
• Write the inequality

X 2
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Try this one on your own or with your
partner Solve
AND graph it
-7y -7y
4 gt y - 10
10 10
14 gt y
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Check out what happens with Division AND
Multiplication
12 gt 4
12 gt 4
THIS IS TRUE
THIS IS TRUE
-3 gt -1
3 gt 1
THIS IS STILL TRUE
NOT TRUE
So something weird happens when we divide by a
negative
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THE RULES

• If you divide OR multiply by a negative number
  you must flip the sign

gt
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Example
x -9
We divided by a negative we have to FLIP
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Solve Graph each Inequality
No Solution It doesnt make sense!
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Solve Graph each Inequality
ALL real numbers are solutions!
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Writing Compound Inequalities
x is greater than 4 and less than or equal to 2.
-6 -5 -4 -3 -2 -1 0
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Writing Compound Inequalities
x is greater than 3 or less than 1.
-2 -1 0 1 2 3 4
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Solving a Compound Inequality with And
Solve the inequality and graph the solution.
-3 -2 -1 0 1 2 3

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Solving a Compound Inequality with And
Solve the inequality and graph the solution.
-5 -4 -3 -2 -1 0 1
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Solving a Compound Inequality with And
Solve the inequality and graph the solution.
-4 -3 -2 -1 0 1 2
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Solving a Compound Inequality with Or
Solve the inequality and graph the solution.
3 4 5 6
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Solving a Compound Inequality with Or
Solve the inequality and graph the solution.
-6 -5 -4 -3 -2 -1 0
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Writing and Using a Linear Model
In 1985, a real estate property was sold for
172,000. The property was sold again in 1999 for
226,000. Write a compound inequality that
represents the different values that the property
was worth between 1995 and 1999.