Isolate

Definition

Isolate, in the context of solving a formula for a specific variable, refers to the process of manipulating an equation to separate or extract the desired variable from the other terms, allowing for its explicit solution.

5 Must Know Facts For Your Next Test

1. Isolating a variable involves performing inverse operations to move all other variables and constants to one side of the equation.
2. The goal of isolating a variable is to obtain an equation where the desired variable is the only term on one side, allowing for its direct solution.
3. Isolating a variable often requires the use of algebraic properties, such as the distributive property, to simplify the equation and separate the target variable.
4. The specific steps to isolate a variable may involve combining like terms, moving terms to the other side of the equation, and performing inverse operations to eliminate the unwanted terms.
5. Isolating a variable is a crucial skill in solving formulas, as it enables you to find the value of a specific variable given the values of the other variables in the equation.

Review Questions

• Explain the purpose of isolating a variable when solving a formula.
  • The purpose of isolating a variable when solving a formula is to manipulate the equation in such a way that the desired variable is the only term on one side of the equation. This allows you to directly solve for the value of that variable, as all other variables and constants have been moved to the other side. Isolating the variable is a crucial step in the problem-solving process, as it enables you to find the value of the specific variable you are interested in.
• Describe the general steps involved in isolating a variable in an equation.
  • The general steps to isolate a variable in an equation are: 1) Identify the variable you want to isolate. 2) Perform inverse operations, such as addition, subtraction, multiplication, or division, to move all other variables and constants to the opposite side of the equation. 3) Simplify the equation by combining like terms and applying algebraic properties, such as the distributive property, to ensure the desired variable is the only term on one side. 4) Verify that the variable is now isolated and can be solved for directly.
• Analyze the importance of isolating variables in the context of solving formulas for a specific variable.
  • Isolating variables is crucial when solving formulas for a specific variable because it allows you to manipulate the equation to obtain a direct solution for the desired variable. By isolating the variable, you can eliminate the influence of all other variables and constants, making it possible to determine the value of the target variable. This skill is essential in a wide range of mathematical and scientific applications, as it enables you to solve for unknown quantities given the values of other variables in a formula. Mastering the process of isolating variables is a fundamental step in developing proficiency in solving formulas for specific variables.

Related terms

Rearrange: The act of reorganizing the terms in an equation to isolate the desired variable.

Solve for: The process of finding the value of a specific variable in an equation or formula.

Algebraic Manipulation:

The use of algebraic operations, such as addition, subtraction, multiplication, and division, to transform an equation into a desired form.