Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Solve. 1. n 42 gt 27 2. r 15 lt 39 3.
17 lt w 52 4. 34 lt m ? 19
n gt 15
r lt 24
35 lt w
53 lt m
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When you multiply or divide both sides of an
inequality by the same positive number, the
statement will still be true. However, when you
multiply or divide both sides by the same
negative number, you need to reverse the
direction of the inequality symbol for the
statement to be true.
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Additional Example 1 Solving Inequalities by
Multiplying
Solve.
t
B. gt 0.3
4
t 4
gt 0.3
t
(4)
Multiply both sides by 4 and reverse the
inequality symbol.
lt (4)0.3
4
t lt 1.2
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Additional Example 2 Solving Inequalities by
Dividing
Solve. Check your answer.
A. 5a 23
5a 23
Divide both sides by 5.
5
5
23 5
3 5
, or 4
a
Check
5a 23
3 5
?
5 is greater than 4 .
5(5) 23

Substitute 5 for a.
?
25 23

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Additional Example 3 Application
It cost Josh 85 to make candles for the craft
fair. How many candles must he sell at 4.00 each
to make a profit?
Since profit is the amount earned minus the
amount spent, Josh needs to earn more than 85.
Let c represent the number of candles that must
be sold.
4c gt 85
Write an inequality.
4c gt 85
Divide both sides by 4.
4 4
c gt 21.25
Josh cannot sell 0.25 candle, so he needs to sell
more than 21 candles to earn a profit.
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Check It Out! Example 1
Solve.
r
B. gt 0.9
3
r 3
gt 0.9
r
(3)
Multiply both sides by 3 and reverse the
inequality symbol.
lt (3)0.9
3
r lt 2.7
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Check It Out! Example 2
Solve. Check your answer.
A. 6b 25
6b 25
Divide both sides by 6.
6
6
25 6
1 6
, or 4
b
Check
6b 25
1 6
6 is greater than 4 .
?
6(6) 25

Substitute 6 for b.
?
36 25

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Check It Out! Example 3
It cost the class 15 to make cookies for the
bake sale. How many cookies must they sell at 10
each to make a profit?
Since profit is the amount earned minus the
amount spent, the class needs to earn more than
15.
Let c represent the number of cookies that must
be sold.
Write an inequality.
0.10c gt 15
0.10c gt 15
Divide both sides by 0.10.
0.10 0.10
c gt 150
The class must sell more than 150 cookies to make
a profit.
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Lesson Quiz
Solve. 1. 2. Solve. Check each answer. 3.
18w lt 4 4. 4f gt 36 5. It costs a candle company
51 to make a dozen candles. How many candles
must it sell at 7 apiece to make a profit?
s 9
gt 12
s gt 108
b 14
b lt 84
gt 6
2 9
w lt
f lt 9
more than 7 candles, or at least 8 candles
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Additional Example 1 Solving Inequalities by
Multiplying
Solve.
c 4
A. 4
c 4
4
c 4
(4)
(4)
(4)
Multiply both sides by 4.
c 16
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Check It Out! Example 1
Solve.
n 6
A. 5
n 6
5
n 6
(5)
(6)
(6)
Multiply both sides by 6.
n 30
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