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The document outlines the properties of inequalities, including the transitive, additive, multiplication, and division properties. It explains how these properties govern the manipulation of inequalities, such as maintaining the direction of the inequality when adding or multiplying by positive numbers, and reversing it when multiplying by negative numbers. Additionally, it mentions the reflexive and symmetric properties, as well as the addition and subtraction properties of inequality.

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19 views2 pages

2

The document outlines the properties of inequalities, including the transitive, additive, multiplication, and division properties. It explains how these properties govern the manipulation of inequalities, such as maintaining the direction of the inequality when adding or multiplying by positive numbers, and reversing it when multiplying by negative numbers. Additionally, it mentions the reflexive and symmetric properties, as well as the addition and subtraction properties of inequality.

Uploaded by

daguisoshema2607
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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PROPERTIES OF INEQUALITY

Inequalities expressions using symbols like <, >, ≤, or ≥, have several properties that
govern how they behave. These properties are crucial for manipulating and solving
inequalities. The main properties include the transitive property, additive property,
multiplication property, and division property.

1. Transitive Property:

If a < b and b < c, then a < c. This means if one quantity is less than a second, and that
second quantity is less than a third, then the first is also less than the third.

This property also applies to >, ≤, and ≥.

2. Additive Property:

Adding the same number to both sides of an inequality doesn't change the inequality's
direction.

If a < b, then a + c < b + c. Similarly, if a > b, then a + c > b + c.

This property also applies to ≤ and ≥.

3. Multiplication and Division Properties:

Multiplying or Dividing by a Positive Number: If a < b and c > 0 (c is positive), then ac < bc.
The inequality sign remains the same.

Multiplying or Dividing by a Negative Number: If a < b and c < 0 (c is negative), then ac >
bc. The inequality sign reverses.

This property also applies to >, ≤, and ≥.

4. Other Important Properties:

Reflexive Property: This property doesn't apply to inequalities. A quantity is not greater
or less than itself.

Symmetric Property: If a < b, then b > a. The inequality sign reverses when the order of
the expressions is reversed.

Addition Property of Inequality: If a < b, then a + c < b + c.

Subtraction Property of Inequality: If a < b, then a - c < b - c.

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