Page 14 - Math Course 3 (Book 1)

Multiplying and Dividing Linear Inequalities
Mo. 1

Lesson 2
Let’s Begin

KEY CONCEPTS:
1. Solve linear inequalities by using Write and Solve an Inequality
multiplication.
2. Solve linear inequalities by using division. Example

MO. 1 - L2a HIKING 3
Bob is walking at a rate of mile per hour. He
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Solving Linear Inequalities: knows that it is at least 9 miles to Onyx Lake. How
Multiplication long will it take Bob to get there? Write and solve

an inequality to find the length of time.
Key Concept 3
4 t ≥ 9 Original inequality
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Multiplying by a 4 3 t ≥ 9 Multiply each side by 4
3
3
4
3
Negative Number
t ≥ 12 Simplify.
Words If each side of a true inequality is
multiplied by the same positive number, 3
the resulting inequality is also true. 4 t ≥ 9; {t | t ≥ 12 };
Answer It would take Bob at least 12
Symbols If a and b are any numbers and c is a hours
positive number, the following are true.
if a > b, then ac > bc and
if a < b, then ac < bc.
This property also holds for inequalities involving
> and < Multiply by a Negative Number

Example

Multiplying by a
Positive Number 3
Solve – d > 6
Words If each side of a true inequality is 5
multiplied by the same negative number, 3
the direction of the inequality symbol – 5 d > 6 Original inequality
must be reversed so that the resulting 5
inequality is also true. – 5 – 3 d > 6 – 5 Multiply each side by – 3
3 5 3 and change > to <
Symbols If a and b are any numbers and c is a d > –10 Simplify
negative number, the following are true.
if a > b, then ac < bc and
if a < b, then ac > bc.
This property also holds for inequalities involving Answer The solution set is {d | d ≤ –10}.
> and <

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