Transcript Holt CA Course 1 - Jefferson School District

11-7 Solving Inequalities by Multiplying or Dividing
California
Standards
Preview of Grade 7
AF4.0 Students
solve simple linear equations and inequalities
over the rational numbers.
Holt CA Course 1
11-7 Solving Inequalities by Multiplying or Dividing
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.
Holt CA Course 1
11-7 Solving Inequalities by Multiplying or Dividing
–4
–2
0
2
2<4
(-1)2
–2
Holt CA Course 1
6
8
10
2 is less than 4.
(-1)4 Multiply both sides by –1.
–4
–2
4
> –4
Use the number line to
determine the correct
inequality symbol.
Reverse the inequality
symbol because –2 is
greater than –4.
11-7 Solving Inequalities by Multiplying or Dividing
Additional Example 1: Solving Inequalities by
Multiplying
Solve.
A. c ≤ –4
4
c ≤ –4
4
(4)c ≤ (4) (–4)
4
c ≤ –16
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Multiply both sides by 4.
11-7 Solving Inequalities by Multiplying or Dividing
Additional Example 1: Solving Inequalities by
Multiplying
Solve.
t
B.
> 0.3
–4
t > 0.3
–4
t
(–4) < (–4)0.3 Multiply both sides by –4
–4
and reverse the inequality
t < –1.2
symbol.
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11-7 Solving Inequalities by Multiplying or Dividing
Additional Example 1B Continued
Check
t
B.
> 0.3
–4
-2 ?
> 0.3
–4
0.5 > 0.3
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–2 is less than –1.2
Substitute –2 for t.
11-7 Solving Inequalities by Multiplying or Dividing
Check It Out! Example 1
Solve.
A. n ≤ –5
6
n ≤ –5
6
(6)n ≤ (6) (–5)
6
n ≤ –30
Holt CA Course 1
Multiply both sides by 6.
11-7 Solving Inequalities by Multiplying or Dividing
Check It Out! Example 1
Solve.
r
B.
> 0.9
–3
r > 0.9
–3
r
(–3) < (–3)0.9 Multiply both sides by –3
–3
and reverse the inequality
r < –2.7
symbol.
Holt CA Course 1
11-7 Solving Inequalities by Multiplying or Dividing
Check It Out! 1B Continued
Check
r
B.
> 0.9
–3
-3 ?
> 0.9
–3
1 > 0.9
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–3 is less than –2.7
Substitute –3 for r.
11-7 Solving Inequalities by Multiplying or Dividing
Additional Example 2: Solving Inequalities by
Dividing
Solve. Check your answer.
A. 5a ≥ 23
5a ≥ 23
Divide both sides by 5.
5
5
23
3
,
or
4
a≥ 5
5
Check
5a ≥ 23
?
5(5) ≥ 23
?
25 ≥ 23
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5 is greater than 4 3 .
5
Substitute 5 for a.
11-7 Solving Inequalities by Multiplying or Dividing
Additional Example 2: Solving Inequalities by
Dividing
Solve. Check your answer.
B. 192< –24b
Check
192 > –24b
–24
–24
–8 > b
Divide both sides by –24,
and reverse the inequality
symbol.
192 < -24b
?
192< -24(–10) –10 is less than –8.
?
192 < 240
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Substitute –10 for b.
11-7 Solving Inequalities by Multiplying or Dividing
Check It Out! Example 2
Solve. Check your answer.
A. 6b ≥ 25
6b ≥ 25
Divide both sides by 6.
6
6
25
1
,
or
4
b≥ 6
6
Check
6b ≥ 25
?
6(6) ≥ 25
?
36 ≥ 25
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6 is greater than 4 1 .
6
Substitute 6 for b.
11-7 Solving Inequalities by Multiplying or Dividing
Check It Out! Example 2
Solve. Check your answer.
B. 85 < –17b
85 > –17b
–17
–17
–5 > b
Divide both sides by –17,
and reverse the inequality
symbol.
Check
85 < –17b
?
85 < –17(–6) –6 is less than –5.
?
85 < 102
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Substitute –6 for b.
11-7 Solving Inequalities by Multiplying or Dividing
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 > 85
Write an inequality.
4c > 85
Divide both sides by 4.
4
4
c > 21.25
Josh cannot sell 0.25 candle, so he needs to sell
more than 21 candles to earn a profit.
Holt CA Course 1
11-7 Solving Inequalities by Multiplying or Dividing
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 > 15
0.10c > 15
Divide both sides by 0.10.
0.10 0.10
c > 150
The class must sell more than 150 cookies to make
a profit.
Holt CA Course 1