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Lesson 64 -- Domain -- Additive Property of Inequality. Domain. Domain – the set of permissible replacement values for the variable in a particular equation or inequality. Fact – every equation and every inequality has a domain*. *If the domain is not stated, it is implied. Domain.

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Domain

Domain – the set of permissible replacement values for the variable in a particular equation or inequality

Fact – every equation and every inequality has a domain*.

*If the domain is not stated, it is implied.

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Domain

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Example 64.1 Graph: x > 2; D = {Real Numbers}

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Domain

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Example 64.2 Graph: ; D = {Integers}

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Domain

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Example 64.3 Graph: ; D = {Reals}

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Domain

Example 64.4 Graph: ; D = {Positive Integers}

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Domain

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Example 64.5 Graph: ; D = {Positive Integers}

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Additive Property of Inequality

The additive property of inequality is like the additive property of equality. We may add something to the left side of an inequality provided that we add the same thing to the right side of the inequality.

Additive Property of Inequality

If a, b, and c are any real numbers such that

a > b

then a + c > b + c and c + a > c + b

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Additive Property of Inequality

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Example 64.6 Graph: ; D = {Reals}

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Additive Property of Inequality

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Example 64.7 Graph: ; D = {Integers}