Math Vocabulary Chapter 6

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Questions and Answers

What does the Addition Property of Equality state?

If you add the same number to each side of an equation, the two sides remain equal. (correct)

When you add a number to both sides of an equation, the equation is no longer true.

You can add different numbers to both sides of an equation.

The sum of both sides must be zero.

What is the definition of the Addition Property of Inequality?

The sum must equal zero.

You can add different numbers to both sides of an inequality.

If you add the same number to both sides of an inequality, the inequality remains true. (correct)

Adding a negative number changes the inequality.

What is a coefficient?

The numerical factor of a term that contains the variable.

What does the Division Property of Equality state?

If you divide each side of an equation by the same number (not 0), the two sides remain equal. Signup and view all the answers

What occurs when you divide each side of an inequality by a negative number?

The inequality symbol must be reversed for it to remain true. Signup and view all the answers

What is an equation?

A mathematical sentence that contains an equals sign (=), stating that two quantities are equal. Signup and view all the answers

What is an equivalent equation?

Two or more equations with the same solution. Signup and view all the answers

What is an inequality?

An open sentence that uses less than, greater than, or other signs to compare two quantities. Signup and view all the answers

What is the Multiplication Property of Equality?

If you multiply each side of an equation by the same number (not 0), the two sides remain equal. Signup and view all the answers

What happens when you multiply each side of an inequality by a negative number?

The inequality symbol must be reversed for it to remain true. Signup and view all the answers

What is a solution in the context of equations?

A replacement value for the variable in an open sentence; a value that makes an equation true. Signup and view all the answers

What does the Subtraction Property of Equality state?

If you subtract the same number from each side of an equation, the two sides remain equal. Signup and view all the answers

What is the Subtraction Property of Inequality?

If you subtract the same number from each side of an inequality, the inequality remains true. Signup and view all the answers

What is a two-step equation?

An equation having two different operations. Signup and view all the answers

What is a two-step inequality?

An inequality that contains two operations. Signup and view all the answers

Study Notes

Properties of Equality and Inequality

Addition Property of Equality: Adding the same number to both sides keeps the equation balanced.
Addition Property of Inequality: Adding the same number to both sides preserves the truth of the inequality.
Division Property of Equality: Dividing both sides by a non-zero number maintains the equality.
Division Property of Inequality: Dividing both sides by a negative number requires reversing the inequality symbol.
Multiplication Property of Equality: Multiplying both sides by a non-zero number keeps the equation equal.
Multiplication Property of Inequality: Multiplying both sides by a negative number necessitates reversing the inequality symbol.
Subtraction Property of Equality: Subtracting the same number from both sides retains the balance of the equation.
Subtraction Property of Inequality: Subtracting the same number from both sides does not affect the truth of the inequality.

Definitions of Key Terms

Coefficient: The numerical factor that appears in front of a variable in an algebraic term.
Equation: A mathematical statement that asserts the equality of two expressions via an equals sign.
Equivalent Equation: Multiple equations that have identical solutions.
Inequality: A statement comparing two quantities using signs for less than, greater than, or their equivalents, rather than an equals sign.
Solution: A value assigned to a variable that makes an equation or inequality true; for example, in the equation 12 = x + 7, the solution is x = 5.

Types of Equations and Inequalities

Two-step Equation: An equation that involves two distinct mathematical operations to solve.
Two-step Inequality: An inequality that requires two operations for resolution.

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Test your knowledge with these vocabulary flashcards for Chapter 6 on Equations and Inequalities. Each card features key terms along with their definitions to help reinforce your understanding. Perfect for students preparing for exams or needing a quick review!