The property of equality that justifies the statement "if -8 + k = -5, then k = 3" is the Addition Property of Equality.
The Addition Property of Equality states that you can add the same value to both sides of an equation without changing its equality. In this case, you can add 8 to both sides of the equation:
-8 + k + 8 = -5 + 8
Simplifying both sides:
k = 3
So, k = 3, and this is justified by the Addition Property of Equality.
The Addition Property of Equality is a fundamental concept in algebra, allowing you to add the same quantity to both sides of an equation without changing its validity. This principle is crucial for manipulating equations, isolating variables, and solving problems. This study guide covers the following topics:
Understanding the Addition Property of Equality: Explains the core concept and its mathematical expression, followed by an example illustrating its application.
Applying the Addition Property: Covers basic equation manipulations, solving simple equations, and combining like terms, fundamental skills in algebra.
Advanced Applications: Explores multi-step equations, equations with fractions, and equations with decimals, providing step-by-step solutions and examples.
Problem-Solving Strategies: Discusses key information identification, developing a plan, and executing the plan, essential for solving mathematical problems systematically.
Practice Problems: Offers equations to solve using the Addition Property of Equality.
Real-World Examples: Shows how this property applies to real-life situations and different fields of study.
Common Mistakes to Avoid: Highlights errors to watch out for when working with equations.
Challenges and Exercises: Presents advanced equations to test and enhance problem-solving skills.
Additional Resources: Recommends books, websites, and tutorials for further study and practice.