Math Problem Statement

tell me about the addition property od equality.

Solution

The Addition Property of Equality is a fundamental principle in algebra that states:

If you add the same number to both sides of an equation, the equality is preserved.

Explanation:

If a=ba = b, then adding the same value cc to both sides results in: a+c=b+ca + c = b + c

This property ensures that the balance of an equation is maintained, which is essential when solving for variables or manipulating equations.

Example:

Given the equation: x5=10x - 5 = 10 To isolate xx, you can apply the Addition Property of Equality by adding 55 to both sides: x5+5=10+5x - 5 + 5 = 10 + 5 Simplifying: x=15x = 15

Application:

  • Solving linear equations.
  • Simplifying expressions to maintain equality.
  • Rearranging formulas.

Would you like a more detailed explanation or examples? Here are some related questions you might explore:

  1. What is the Subtraction Property of Equality?
  2. How does the Addition Property of Equality apply to solving inequalities?
  3. Can the Addition Property of Equality be used with fractions or decimals?
  4. What role does the Addition Property of Equality play in systems of equations?
  5. How do we combine the Addition Property with other algebraic properties?

Tip: Always perform the same operation on both sides of the equation to maintain balance!

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Math Problem Analysis

Mathematical Concepts

Algebra
Properties of Equality

Formulas

If a = b, then a + c = b + c

Theorems

Addition Property of Equality

Suitable Grade Level

Grades 6-8