Example

Simplifying 4y9+94y - 9 + 9 Using the Inverse Property of Addition

To simplify the expression 4y9+94y - 9 + 9, observe that the constant terms 9-9 and +9+9 are additive inverses of each other. By the inverse property of addition, 9+9=0-9 + 9 = 0. Therefore:

4y9+9=4y+0=4y4y - 9 + 9 = 4y + 0 = 4y

The variable term 4y4y is unaffected because adding zero to any quantity leaves it unchanged (the identity property of addition). This type of simplification is a foundational skill for solving equations: when the same number is added to and subtracted from the same side of an equation, those operations cancel each other out, leaving only the remaining terms. Recognizing additive inverse pairs within an expression allows for quicker simplification without needing to combine terms step by step.

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Updated 2026-04-21

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