Questions and Answers
What is the absolute value of a number, x?
What is the additive inverse of a?
-a
An algebraic expression can contain numbers but no variables.
False
What does a coefficient refer to?
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How can you form a compound inequality?
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A constant is a quantity that can change.
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What is a constant term?
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What is an equation?
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What does it mean to evaluate an algebraic expression?
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An extraneous solution is a valid solution of the original equation.
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What is an identity in terms of equations?
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What are inverse operations?
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Like terms can have different variables raised to the same powers.
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What is a literal equation?
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What is the multiplicative inverse of a nonzero number a?
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A numerical expression can include letters.
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What is the opposite of a?
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What is a solution of an equation?
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What constitutes a term of an expression?
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What is a variable?
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What is a variable quantity?
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How can you represent patterns?
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What are the subsets of real numbers?
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What are the properties used to simplify and evaluate expressions?
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How do you evaluate an algebraic expression?
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What must you consider when rewriting equations with absolute values?
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Study Notes
Key Algebra Concepts
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Absolute Value: Represented as |x|, signifies the distance of x from zero on the number line.
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Additive Inverse: The additive inverse of a number a is -a; their sum equals zero, the additive identity.
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Algebraic Expression: A mathematical phrase containing one or more variables, representing a relationship between quantities.
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Coefficient: The numerical factor that multiplies a variable in a term, crucial for identifying terms in expressions.
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Compound Inequality: Two inequalities combined using and or or, allowing for complex relationships between variables.
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Constant: A value that remains unchanged, important in equations and expressions.
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Constant Term: A term in an expression that contains no variables, contributing to the value of the expression.
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Equation: A statement that asserts the equality of two algebraic expressions, fundamental in problem-solving.
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Evaluate: The process of substituting values for variables in an expression and simplifying the result using order of operations.
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Extraneous Solution: A solution that arises during solving an equation but does not satisfy the original equation.
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Identity: An equation that holds true for every possible value of a variable, essential for verifying mathematical statements.
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Inverse Operations: Operations that reverse each other; for example, addition and subtraction or multiplication and division.
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Like Terms: Terms that share the same variables raised to the same powers, which can be combined during simplification.
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Literal Equation: An equation involving multiple letters as variables, commonly seen in formulas and relations.
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Multiplicative Inverse: The reciprocal, 1/a, of a nonzero number a; when multiplied together, they yield the multiplicative identity, 1.
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Numerical Expression: A collection of numbers and operation symbols, simpler than algebraic expressions since they lack variables.
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Opposite: Identical to the additive inverse; the sum of a number and its opposite is zero.
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Reciprocal: Another term for the multiplicative inverse; the reciprocal of a number multiplied by that number equals one.
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Solution of an Equation: A value that satisfies the equation, making both sides equal.
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Term of an Expression: Can be a number, variable, or a product of both, forming the building blocks of expressions.
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Variable: A symbol, typically a letter, representing one or more numbers, essential in algebra for generalizing equations.
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Variable Quantity: A variable that can take on different values, highlighting the dynamic nature of algebra.
Lessons Overview
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Lesson 1: Patterns and Expressions: Patterns can be expressed using various forms; identifying patterns involves recognizing consistent changes and can be assisted by tables.
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Lesson 2: Properties of Real Numbers: Real numbers include natural, whole, integer, rational, and irrational numbers. Significant properties include:
- Commutative Properties: Addition and multiplication can be performed in any order.
- Associative Properties: The grouping of numbers does not affect the result in addition and multiplication.
- Distributive Property: Allows expansion of expressions involving addition within parentheses.
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Lessons 3, 4, and 5: Expressions, Equations, and Inequalities:
- To evaluate an expression, substitute values for variables.
- Simplification involves combining like terms.
- Solutions to equations and inequalities rely on the properties of equality and inequality.
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Lesson 6: Absolute Value Equations and Inequalities:
- When dealing with absolute values, consider both positive and negative cases to achieve complete solutions.
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Description
Test your understanding of fundamental algebra concepts such as absolute value, coefficients, and equations. This quiz covers essential definitions and examples that are crucial for mastering algebra. Whether you're a beginner or looking to refresh your skills, this quiz is designed to reinforce your knowledge.
