key term - Addition Property of Equality

Definition

The addition property of equality states that if two expressions are equal, then adding the same number to both expressions will result in two new expressions that are also equal. This property allows for the manipulation of linear equations by adding or subtracting the same value to both sides to isolate the variable and find the solution.

5 Must Know Facts For Your Next Test

1. The addition property of equality allows you to add the same number to both sides of an equation without changing the solution.
2. This property is often used in the general strategy for solving linear equations, where you isolate the variable by performing inverse operations.
3. Adding the same value to both sides of an equation is a way to maintain the balance and equality between the two expressions.
4. The addition property of equality is a fundamental principle that enables you to simplify and solve linear equations step-by-step.
5. Understanding and applying the addition property of equality is crucial for successfully solving a wide range of linear equation problems.

Review Questions

• Explain how the addition property of equality can be used to solve a linear equation.
  • The addition property of equality states that if two expressions are equal, then adding the same number to both expressions will result in two new expressions that are also equal. This property is essential for solving linear equations, as it allows you to isolate the variable term by adding or subtracting the same value to both sides of the equation. By performing these inverse operations, you can simplify the equation and find the value of the variable that satisfies the original equation.
• Describe the relationship between the addition property of equality and the general strategy for solving linear equations.
  • The addition property of equality is a key component of the general strategy for solving linear equations. This strategy involves performing a series of steps to isolate the variable term, and the addition property is often used in the early stages of this process. By adding the same value to both sides of the equation, you can eliminate terms and move the variable to one side, making it easier to find the solution. The addition property of equality is a fundamental principle that enables you to maintain the balance and equality between the two sides of the equation throughout the solving process.
• Analyze how the addition property of equality helps ensure the validity of the solution when solving linear equations.
  • The addition property of equality is crucial for ensuring the validity of the solution when solving linear equations. By adding the same value to both sides of the equation, you are preserving the equality between the expressions, which means that any steps taken to isolate the variable will not change the underlying solution. This property allows you to perform inverse operations, such as adding or subtracting values, without altering the original relationship between the variables and constants. By consistently applying the addition property of equality, you can be confident that the final solution satisfies the original linear equation and is a valid answer.

Related terms

Linear Equation:

An equation in which the highest exponent of the variable is 1, and the variables are raised to the first power.

Isolate the Variable:

The process of rearranging an equation to get the variable term on one side and all other terms on the other side.

Inverse Operations:

Operations that undo each other, such as addition and subtraction, or multiplication and division.