Algebra Class Flashcards: Expressions & Equations

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Questions and Answers

What is the Addition Property of Equality?

If you subtract the same number from both sides of an equation, the new equation will have the same solution.

If you add the same number to both sides of an equation, the new equation will have the same solution. (correct)

If you multiply both sides of an equation by the same number, the new equation will have the same solution.

If you divide both sides of an equation by the same number, the new equation will have the same solution.

What is an algebraic expression?

It contains one or more variables and may contain operation symbols.

What is a coefficient?

A number that is multiplied by a variable in an algebraic expression.

What is a constant?

A value that does not change. Signup and view all the answers

What does the Division Property of Equality state?

If you divide both sides of an equation by the same nonzero number, the new equation will have the same solution. Signup and view all the answers

What is an equation?

A mathematical statement that two quantities are equal. Signup and view all the answers

What is an equivalent expression?

Expressions that have the same value for all values of the variables. Signup and view all the answers

What does evaluate mean in mathematics?

To find the value of a numerical expression. Signup and view all the answers

What is an expression?

A mathematical phrase that contains operations, numbers, and/or variables. Signup and view all the answers

What are inverse operations?

Operations that undo each other. Signup and view all the answers

What are like terms?

Two or more terms that have the same variable raised to the same power. Signup and view all the answers

What does the Multiplication Property of Equality state?

If you multiply both sides of an equation by the same number, the new equation will have the same solution. Signup and view all the answers

What does simplify mean?

To write a fraction or expression in simplest form. Signup and view all the answers

What is a solution in algebra?

If a value for a variable makes an equation true, that value is a solution of the equation. Signup and view all the answers

What is a solution of an equation or inequality?

A value or values that make the equation or inequality true. Signup and view all the answers

What does substitute mean?

To replace a variable with a number or another expression in an algebraic expression. Signup and view all the answers

What does the Subtraction Property of Equality state?

If you subtract the same number from both sides of an equation, the new equation will have the same solution. Signup and view all the answers

What is a term in a mathematical expression?

A number, a variable, or a product of numbers and variables. Signup and view all the answers

What is a variable?

A letter or symbol that represents a quantity that can change. Signup and view all the answers

Study Notes

Algebraic Expressions & Equations Concepts

Addition Property of Equality: Adding the same number to both sides of an equation keeps the solution unchanged.
Algebraic Expression: Comprises one or more variables along with operational symbols.
Coefficient: A number multiplying a variable in an expression; for instance, in 4a + 2, the coefficient is 4.
Constant: A fixed value that does not vary.
Division Property of Equality: Dividing both sides of an equation by the same nonzero number maintains the original solution.
Equation: Formulates a mathematical assertion that equates two quantities.
Equivalent Expression: Expressions that hold identical value across all variable inputs, such as 4x + 5x and 9x.
Evaluate: The process of determining the value of a numerical expression.
Expression: A mathematical phrase featuring operations, numbers, and/or variables; for example, 5x + 2.
Inverse Operations: Operations that negate one another, including addition and subtraction, or multiplication and division.
Like Terms: Terms that share the same variable raised to identical powers, exemplified by 3a and 12a in the expression 3a + 5b + 12a.
Multiplication Property of Equality: Multiplying both sides of an equation by the same number preserves its solution.
Simplify: The act of rewriting a fraction or algebraic expression in its most straightforward form.
Solution: A variable value that satisfies an equation, making it true.
Solution of an Equation or Inequality: Specific value(s) that validate the given equation or inequality.
Substitute: To replace a variable within an algebraic expression with a designated number or expression.
Subtraction Property of Equality: Subtracting the same number from both sides of an equation retains the solution.
Term: Refers to a number, variable, or multiplication of numbers and variables, delineated by plus or minus signs in expressions.
Variable: A symbol or letter that signifies a quantity subject to change.

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Description

This quiz features key terms related to algebraic expressions and equations, perfect for mastering foundational concepts in algebra. Each flashcard provides a definition to help understand and apply the concepts effectively.