holt ca course 1 11-7 solving inequalities by multiplying or dividing preview of grade 7 af4.0...

Holt CA Course 1

11-7 Solving Inequalities by Multiplying or Dividing

Preview of Grade 7 AF4.0 Students solve simple linear equations and inequalities over the rational numbers.

California Standards

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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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2 < 4

–4

(1)2 (1)4

–2 >> –4

–2

2 is less than 4.

Multiply both sides by –1.

Use the number line to determine the correct inequality symbol.

Reverse the inequality symbol because –2 is greater than –4.

–4 –2 0 2 4 6 8 10

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Solve.

Additional Example 1: Solving Inequalities by Multiplying

c4A. ≤ –4

c4 ≤ –4

c4 ≤ (–4)(4) (4)

c ≤ –16

Multiply both sides by 4.

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Solve.

Additional Example 1: Solving Inequalities by Multiplying

tB. > 0.3

t–4

> 0.3

t< (–4)0.3(–4)

t < –1.2

–4

–4Multiply both sides by –4 and reverse the inequalitysymbol.

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Check

Additional Example 1B Continued

tB. > 0.3–4

–2 is less than –1.2 Substitute –2 for t.

2–4

> 0.3?

0.5 > 0.3

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Solve.

n6A. ≤ –5

n6 ≤ –5

n6 ≤ (–5)(6) (6)

n ≤ –30

Multiply both sides by 6.

Check It Out! Example 1

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Solve.

rB. > 0.9

r–3

> 0.9

r< (–3)0.9(–3)

r < –2.7

–3

–3Multiply both sides by –3 and reverse the inequalitysymbol.


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Check

Check It Out! 1B Continued

rB. > 0.9–3

–3 is less than –2.7 Substitute –3 for r.

3–3

> 0.9?

1 > 0.9

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Solve. Check your answer.

Additional Example 2: Solving Inequalities by Dividing

A. 5a ≥ 235a ≥ 235 5

a ≥ 235

Divide both sides by 5.

, or 4 35

Check5a ≥ 23

5(5) 23≥?

25 23≥?

5 is greater than 4 . 35

Substitute 5 for a.

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Additional Example 2: Solving Inequalities by Dividing

B. 192< –24b

192 > –24b–24 –24

–8 > b

Divide both sides by –24, and reverse the inequality symbol.

Check192 < 24b

192< 24(–10)?

? 192 < 240

–10 is less than –8. Substitute –10 for b.

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A. 6b ≥ 256b ≥ 256 6

b ≥ 256


, or 4 16

Check6b ≥ 25

6(6) 25≥?

36 25≥?

6 is greater than 4 . 16

Substitute 6 for b.


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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)?

? 85 < 102

–6 is less than –5. Substitute –6 for b.

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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?

Additional Example 3: Application

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

4c > 854 4

c > 21.25

Josh cannot sell 0.25 candle, so he needs to sell more than 21 candles to earn a profit.

Write an inequality.


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Check It Out! Example 3It 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. 0.10c > 15

0.10c > 150.10 0.10

c > 150The class must sell more than 150 cookies to make a profit.

Write an inequality.

Divide both sides by 0.10.

holt ca course 1 11-7 solving inequalities by multiplying or dividing preview of grade 7 af4.0...

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