key term - Subtraction Property of Equality

Definition

The subtraction property of equality states that if the same number is subtracted from both sides of an equation, the equality is still maintained. This property allows for the simplification and solving of linear equations by isolating the variable on one side of the equation.

5 Must Know Facts For Your Next Test

1. The subtraction property of equality allows you to subtract the same number from both sides of an equation, maintaining the equality.
2. This property is particularly useful when solving linear equations, as it allows you to isolate the variable term on one side of the equation.
3. The subtraction property of equality is often used in conjunction with the addition property of equality to simplify and solve equations.
4. Correctly applying the subtraction property of equality is essential for solving a wide range of linear equations, including those involving integers and other operations.
5. Understanding the subtraction property of equality is a fundamental skill for success in topics such as 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality, 3.5 Solve Equations Using Integers; The Division Property of Equality, and 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality.

Review Questions

• Explain how the subtraction property of equality can be used to solve a linear equation.
  • To use the subtraction property of equality to solve a linear equation, you would first identify the variable term and the constant terms on each side of the equation. Then, you would subtract the same constant from both sides of the equation, effectively isolating the variable term on one side. This allows you to solve for the variable and find the solution to the equation.
• Describe how the subtraction property of equality relates to the addition property of equality in the context of solving linear equations.
  • The subtraction property of equality and the addition property of equality work hand-in-hand when solving linear equations. The subtraction property allows you to isolate the variable term by subtracting the same constant from both sides, while the addition property allows you to move constant terms to the other side of the equation. By strategically applying these two properties, you can systematically simplify the equation and solve for the unknown variable.
• Analyze how the understanding of the subtraction property of equality is essential for success in topics such as 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality, 3.5 Solve Equations Using Integers; The Division Property of Equality, and 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality.
  • The subtraction property of equality is a fundamental concept that underpins the ability to solve linear equations, which is a crucial skill in topics like 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality, 3.5 Solve Equations Using Integers; The Division Property of Equality, and 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality. By understanding how to apply the subtraction property to isolate variables and simplify equations, you can effectively solve a wide range of linear equations, including those involving integers and other operations. Mastering the subtraction property of equality is essential for success in these topics and for developing a strong foundation in algebra.

Related terms

Addition Property of Equality:

The addition property of equality states that if the same number is added to both sides of an equation, the equality is still maintained. This property, along with the subtraction property, is used to solve linear equations.

Linear Equation:

A linear equation is an equation in which the variable terms have an exponent of 1. Linear equations can be solved using the addition and subtraction properties of equality.

Isolating the Variable:

Isolating the variable refers to the process of manipulating an equation to get the variable term on one side, usually the left side, and all other terms on the other side. This is a key step in solving linear equations.