key term - Isolation Method

Definition

The isolation method is a technique used to solve linear equations with variables and constants on both sides of the equation. It involves isolating the variable of interest on one side of the equation by performing inverse operations to eliminate the other variables and constants.

5 Must Know Facts For Your Next Test

1. The isolation method is particularly useful for solving linear equations with variables and constants on both sides of the equation.
2. To use the isolation method, you need to perform inverse operations to isolate the variable of interest on one side of the equation.
3. The inverse operations used in the isolation method include addition, subtraction, multiplication, and division.
4. Applying the isolation method correctly ensures that the variable of interest is the only term remaining on one side of the equation.
5. The isolation method allows you to find the value of the variable that satisfies the equation.

Review Questions

• Explain how the isolation method can be used to solve a linear equation with variables and constants on both sides.
  • To use the isolation method to solve a linear equation with variables and constants on both sides, you need to perform inverse operations to isolate the variable of interest on one side of the equation. This typically involves adding, subtracting, multiplying, or dividing the equation to eliminate the other variables and constants, leaving only the variable you want to solve for on one side. By applying the appropriate inverse operations, you can isolate the variable and find its value that satisfies the equation.
• Describe the role of inverse operations in the isolation method.
  • Inverse operations play a crucial role in the isolation method. Inverse operations, such as addition and subtraction or multiplication and division, are used to undo the operations on the variable of interest and isolate it on one side of the equation. For example, if the equation has a variable multiplied by a constant on one side, you would need to divide both sides of the equation by that constant to isolate the variable. The use of inverse operations is essential in the isolation method to eliminate the other variables and constants and leave only the variable you want to solve for on one side of the equation.
• Analyze how the isolation method can be applied to solve a more complex linear equation with variables and constants on both sides.
  • To apply the isolation method to a more complex linear equation with variables and constants on both sides, you would need to carefully identify the appropriate inverse operations to perform. This may involve a sequence of steps, such as first isolating one variable, then using that variable to isolate another, and so on, until you have isolated the variable of interest. The key is to systematically apply inverse operations to eliminate the other variables and constants, one by one, until you are left with the variable you want to solve for on one side of the equation. This methodical approach, using the appropriate inverse operations, is the essence of the isolation method and allows you to solve even complex linear equations with variables and constants on both sides.

Related terms

Inverse Operations:

Inverse operations are mathematical operations that undo each other, such as addition and subtraction or multiplication and division.

Linear Equation:

A linear equation is an equation in which the highest exponent of the variable is 1, and the variables and constants are connected by addition, subtraction, multiplication, or division.

Variable:

A variable is a symbol, usually a letter, that represents an unknown or changeable quantity in a mathematical expression.