Learn to solve inequalities with rational numbers'

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Learn to solve inequalities with rational
numbers.
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Vocabulary
(Taken from lesson 3-1)
rationalonumber
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(Taken from lesson 3-1)
Decimals that terminate or repeat are rational
numbers.
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(Taken from lesson 3-1)
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Additional Examples 1 Solving Inequalities with
Decimals
Solve.
A. 0.4x ? 0.8
Divide both sides by 0.4 .
x ? 2
B. y 3.8 lt 11
Add 3.8 to both sides of the equation.
y 3.8 3.8 lt 11 3.8
y lt 14.8
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Try This Examples 1
Solve.
A. 0.6y ? 1.8
Divide both sides by 0.6 .
y ? 3
B. m 4.2 lt 15
Add 4.2 to both sides of the equation.
m 4.2 4.2 lt 15 4.2
m lt 19.2
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Additional Example 2A Solving Inequalities with
Fractions
Solve.
A.
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Additional Example 2B Solving Inequalities with
Fractions Continued
Solve.
1 4
2 n ? 9
B.
n ? 4
Change ? to ?.
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Try This Example 2A
Solve.
1 5
v gt 7
A.
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Try This Example 2B
Solve.
2 5
1 j 7
B.
j 5
Change ? to ?.
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Additional Example 3 Problem Solving Application
The height of an envelope is 3.8 in. What are the
minimum and maximum lengths to avoid an extra
charge?
With first-class mail, there is an extra charge
in any of these cases
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Additional Example 3 Continued
The answer is the minimum and maximum lengths for
an envelope to avoid an extra charge. List the
important information The height of the piece
of mail is 3.8 inches. If the length divided by
the height is between 1.3 and 2.5, there will not
be an extra charge.
Show the relationship of the information
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Additional Example 3 Continued
You can use the model from the previous slide to
write an inequality where l is the length and 3.8
is the height.
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Additional Example 3 Continued
Multiply both sides of each inequality by 3.8.
3.8 1.3 l and l 2.5 3.8
l ? 4.94 and l 9.5
Simplify.
The length of the envelope must be between 4.94
in. and 9.5 in.
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Additional Example 3 Continued
4.94 ? 3.8 1.3 and 9.5 ? 3.8 2.5, so there
will not be an extra charge.
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Try This Example 3
The height of an envelope is 4.9 in. What are the
minimum and maximum lengths to avoid an extra
charge?
With first-class mail, there is an extra charge
in any of these cases
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Try This Example 3 Continued
The answer is the minimum and maximum lengths for
an envelope to avoid an extra charge. List the
important information The height of the piece
of mail is 4.9 inches. If the length divided by
the height is between 1.3 and 2.5, there will not
be an extra charge.
Show the relationship of the information
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Try This Example 3 Continued
You can use the model from the previous slide to
write an inequality where l is the length and 4.9
is the height.
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Try This Example 3 Continued
Multiply both sides of each inequality by 4.9.
4.9 1.3 l and l 2.5 4.9
l ? 6.37 and l 12.25
Simplify.
The length of the envelope must be between 6.37
in. and 12.25 in.
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Try This Example 3 Continued
6.37 ? 4.9 1.3 and 12.25 ? 4.9 2.5, so there
will not be an extra charge.
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Lesson Quiz Part 1
Solve.
1. w 1.25 ? 5.12
w 3.87
1 4
3 8
2. f 1 ? 4
x gt 14.2
3. 1.2x gt 17.04

h 0.7
4.
lt 5.5
h lt 3.85
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Lesson Quiz Part 2
Rosas car gets between 20 and 21 mi/gal on the
highway. She knows that her gas tank holds at
least 18 gallons. What is the minimum distance
Rosa could drive her car on the highway between
fill-ups?
5.
360 miles