Algebra Chapter 3: Equations and Inequalities

Questions and Answers

What are equivalent equations?

Equations with variables on both sides

Equations that have different solutions

Equations that have the same solution (correct)

Equations that are always true

What is the addition property of equality?

If a = b, then a + c = b + c. You can add the same number to both sides of an equation without changing its equality.

What is the subtraction property of equality?

If a = b, then a - c = b - c.

What is the multiplication property of equality?

If a = b, then ac = bc. Signup and view all the answers

What is the division property of equality?

If a = b and c is not equal to 0, then a/c = b/c. Signup and view all the answers

What is an inequality?

A statement that compares two quantities using <, ≤, ≥, or ≠. Signup and view all the answers

What is a solution set of an inequality?

The set of all of the values of a variable that make an inequality true. Signup and view all the answers

What are equivalent inequalities?

Inequalities that have the same set of solutions. Signup and view all the answers

What happens when you multiply or divide an inequality by a negative number?

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

Study Notes

Algebraic Equations and Inequalities

Equivalent Equations: Solutions are identical for these equations, meaning they yield the same result when values are substituted.
Addition Property of Equality: States that adding the same value to both sides of an equation does not change the equality; mathematically represented as if a = b, then a + c = b + c.
Subtraction Property of Equality: Similar to the addition property, it allows subtraction of the same value from both sides of an equation; if a = b, then a - c = b - c.
Multiplication Property of Equality: When both sides of an equation are multiplied by the same non-zero value, equality is maintained; expressed as if a = b, then ac = bc.
Division Property of Equality: This property allows division of both sides by the same non-zero number, ensuring the equation remains balanced; if a = b and c ≠ 0, then a/c = b/c.
Inequality: Defines a relationship between two quantities that are not necessarily equal, utilizing symbols such as <, ≤, ≥, or ≠.
Solution Set of an Inequality: Represents all possible values that can satisfy an inequality, providing a complete range of acceptable solutions for a variable.
Equivalent Inequalities: These inequalities share the same solution set, meaning they will yield the same results when graphed or solved.
Multiplication/Dividing an Inequality by a Negative: When an inequality is multiplied or divided by a negative number, the inequality sign must be flipped to maintain a truthful comparison.

Description

Test your knowledge of algebraic equations and inequalities with these flashcards. This quiz covers key concepts including equivalent equations and properties of equality. Perfect for reinforcing your understanding of foundational algebra concepts.