Subtraction Property of Equality

Definition

The subtraction property of equality states that if you subtract the same quantity from both sides of an equation, the equality will still hold true. This property allows you to isolate variables and solve for unknown values in an equation.

5 Must Know Facts For Your Next Test

1. The subtraction property of equality allows you to move terms containing variables to one side of the equation.
2. Subtracting the same quantity from both sides of an equation does not change the solution to the equation.
3. Using the subtraction property is a key step in solving multi-step equations by isolating the variable.
4. The subtraction property is often used in conjunction with the addition property to simplify equations.
5. Proper use of the subtraction property is essential for solving a wide variety of linear equations.

Review Questions

• Explain how the subtraction property of equality can be used to isolate a variable in an equation.
  • The subtraction property of equality states that if you subtract the same quantity from both sides of an equation, the equality will still hold true. This allows you to move terms containing variables to one side of the equation, effectively isolating the variable. By subtracting terms from both sides, you can systematically eliminate all the terms on one side except for the variable, making it easier to solve for the unknown value.
• Describe the relationship between the subtraction property of equality and the addition property of equality, and how they can be used together to solve equations.
  • The subtraction property of equality and the addition property of equality work hand-in-hand when solving equations. The subtraction property allows you to isolate variables by moving terms to one side, while the addition property allows you to combine like terms on each side. By using these properties in tandem, you can systematically simplify an equation until you are left with the variable on one side and the solution on the other. This step-by-step process of using the addition and subtraction properties is a fundamental technique for solving a wide variety of linear equations.
• Evaluate the importance of the subtraction property of equality in the context of solving equations using the addition and subtraction properties, and explain how mastery of this concept can benefit a student's success in algebra.
  • The subtraction property of equality is a crucial concept in solving equations using the addition and subtraction properties. Without the ability to isolate variables by subtracting the same quantity from both sides, the process of solving equations would be significantly more complex and challenging. Mastery of the subtraction property allows students to systematically simplify equations, moving closer to the solution step-by-step. This foundational skill is essential for success in algebra, as it underpins the ability to solve a wide range of linear equations, which are the building blocks for more advanced algebraic concepts. By fully understanding and applying the subtraction property of equality, students can develop the algebraic fluency and problem-solving skills necessary to excel in their algebra coursework and beyond.

Related terms

Addition Property of Equality: The addition property of equality states that if you add the same quantity to both sides of an equation, the equality will still hold true.

Isolating Variables: The process of manipulating an equation to get a variable on one side by itself, using the addition and subtraction properties of equality.

Solving Equations: The process of finding the value of the unknown variable in an equation by using algebraic operations and properties.