key term - Isolation Method

Definition

The isolation method is a technique used to solve linear equations by systematically isolating the variable on one side of the equation. This method involves performing inverse operations to isolate the variable and find its value, ensuring that the equation remains balanced on both sides.

5 Must Know Facts For Your Next Test

1. The isolation method is a fundamental technique used to solve linear equations with variables on both sides.
2. The key steps in the isolation method are to use the division and multiplication properties of equality to isolate the variable on one side of the equation.
3. Inverse operations, such as addition and subtraction or multiplication and division, are used to isolate the variable.
4. The isolation method ensures that the equation remains balanced and the solutions obtained are valid.
5. Applying the isolation method correctly is crucial for solving a wide range of linear equations, including those with variables and constants on both sides.

Review Questions

• Explain how the isolation method can be used to solve an equation with variables and constants on both sides.
  • To solve an equation with variables and constants on both sides using the isolation method, you would first identify the variable you want to isolate. Then, you would perform inverse operations, such as division or multiplication, to move all the terms with the variable to one side of the equation and all the constant terms to the other side. This would effectively isolate the variable, allowing you to solve for its value and ensure the equation remains balanced on both sides.
• Describe the role of the division and multiplication properties of equality in the isolation method.
  • The division and multiplication properties of equality are essential to the isolation method. The division property states that if an equation is divided by the same non-zero number on both sides, the resulting equation is still true. Similarly, the multiplication property states that if an equation is multiplied by the same non-zero number on both sides, the resulting equation is still true. By applying these properties, you can systematically isolate the variable on one side of the equation, ensuring that the equation remains balanced and the solution is valid.
• Analyze how the use of inverse operations, such as addition and subtraction or multiplication and division, helps to solve equations using the isolation method.
  • Inverse operations are crucial in the isolation method because they allow you to undo the operations performed on the variable and isolate it on one side of the equation. For example, if an equation has the variable multiplied by a constant on one side, you can divide both sides by that constant to isolate the variable. Similarly, if the variable is added to a constant on one side, you can subtract that constant from both sides to isolate the variable. By strategically applying inverse operations, you can systematically isolate the variable and solve the equation while maintaining the balance on both sides.

Related terms

Division Property of Equality:

The division property of equality states that if an equation is divided by the same non-zero number on both sides, the resulting equation is still true.

Multiplication Property of Equality:

The multiplication property of equality states that if an equation is multiplied by the same non-zero number on both sides, the resulting equation is still true.

Inverse Operations:

Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division. They are used to isolate the variable in an equation.