Inverse Operations and Properties of Equality
Inverse operations and properties of equality is a Grade 6 algebra skill in Big Ideas Math Advanced 1, Chapter 7: Equations and Inequalities. Inverse operations undo each other (addition/subtraction, multiplication/division), and the properties of equality ensure that applying the same inverse operation to both sides of an equation maintains balance and reveals the solution.
Key Concepts
Addition and subtraction are inverse operations that undo each other: $a + b b = a$ and $a b + b = a$.
Properties of Equality maintain balance: Addition Property: If $a = b$, then $a + c = b + c$ Subtraction Property: If $a = b$, then $a c = b c$.
Common Questions
What are inverse operations?
Inverse operations are operations that undo each other. Addition and subtraction are inverses (5 + 3 - 3 = 5). Multiplication and division are inverses (4 x 6 / 6 = 4). Using inverse operations to both sides of an equation isolates the variable.
How do properties of equality help solve equations?
The properties of equality state you can add, subtract, multiply, or divide both sides of an equation by the same number without changing the solution. This allows you to apply inverse operations to isolate the variable.
What is an example of using inverse operations to solve an equation?
To solve x + 7 = 12, use the inverse of addition (subtraction): subtract 7 from both sides. x + 7 - 7 = 12 - 7, so x = 5. Check: 5 + 7 = 12. Correct!
Where is this skill taught in Big Ideas Math Advanced 1?
Inverse operations and properties of equality are covered in Chapter 7: Equations and Inequalities of Big Ideas Math Advanced 1, the Grade 6 math textbook.