Questions and Answers
What is an equation?
What are equivalent equations?
Equations that have the same solution
What are inverse operations?
An operation that reverses the effect of another operation
What is a null set?
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What is a solution in terms of equations?
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What is a two-step equation?
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What is a constant?
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What is a coefficient?
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What is a variable?
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Using the Distributive Property, a(b + c) = _____ + _____
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What is the Multiplication Property of Equality?
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What is the Division Property of Equality?
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What is the Addition Property of Equality?
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What is the Subtraction Property of Equality?
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What is a reciprocal?
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What is an inequality?
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Study Notes
Key Mathematical Terms and Concepts
- Equation: A mathematical sentence indicating that two expressions are equal.
- Equivalent Equations: Different equations that yield the same solution, demonstrating equality in their respective outputs.
- Inverse Operations: Operations that counteract the effect of others, such as addition and subtraction or multiplication and division.
Sets and Solutions
- Null Set: A specific type of set that contains no elements, often represented by the symbol ∅.
- Solution: A value that satisfies an equation, making it true; for instance, both y + 8 = 10 and y = 18 have equivalent solutions.
Types of Equations
- Two-Step Equation: An equation requiring two distinct operations to isolate the variable; example: 2x + 3 = 7.
Constants and Variables
- Constant: A fixed value that does not contain a variable; represents a single number.
- Coefficient: A numerical factor multiplied by a variable within an algebraic expression.
Variables
- Variable: Typically a letter symbolizing one or more unknown numbers in mathematical expressions.
Properties of Equality and Operations
- Distributive Property: A key principle allowing the distribution of multiplication over addition, articulated as a(b + c) = ab + ac.
- Multiplication Property of Equality: States that multiplying both sides of an equation by the same nonzero number maintains the equality.
- Division Property of Equality: Indicates that dividing both sides of an equation by the same nonzero number keeps the equality intact.
- Addition Property of Equality: Establishes that adding the same number to both sides of an equation preserves equality.
- Subtraction Property of Equality: Confirms that subtracting the same number from both sides of an equation results in equality.
Additional Concepts
- Reciprocal: The multiplicative inverse of a number; when multiplied with the original number, yields the product of 1.
- Inequality: A formulative statement that expresses the comparison between two quantities using symbols like <, ≤, ≥, or ≠.
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Description
Test your knowledge with these flashcards focused on key mathematical concepts from Accelerated Math Chapter 8. Each card features important terms like equations, equivalent equations, and inverse operations, helping you strengthen your understanding of algebra. Perfect for students looking to review essential definitions on the fly!
