key term - Checking the Solution

Definition

Checking the solution is the process of verifying that the proposed solution satisfies the original equation or problem statement. It involves substituting the solution back into the original equation to ensure that it holds true and accurately solves the problem.

5 Must Know Facts For Your Next Test

1. Checking the solution is an essential step in the problem-solving process, as it ensures the proposed solution is correct and satisfies the original equation.
2. The process of checking the solution involves substituting the proposed values for the variables back into the original equation and verifying that the equation is true.
3. Checking the solution can help identify any errors or mistakes made during the problem-solving process, allowing for corrections and a more accurate final result.
4. Thoroughly checking the solution can also provide valuable insights into the problem-solving strategy and the relationships between the variables and the equation.
5. Checking the solution is particularly important when dealing with complex or multi-step equations, as it helps to confirm that the intermediate steps were performed correctly.

Review Questions

• Explain the purpose of checking the solution when solving linear equations.
  • The purpose of checking the solution when solving linear equations is to verify that the proposed solution satisfies the original equation. By substituting the values for the variables back into the equation, you can confirm that the equation holds true and the solution accurately solves the problem. Checking the solution is a crucial step in the problem-solving process, as it helps to identify any errors or mistakes made during the intermediate steps and ensures the final result is correct.
• Describe the process of checking the solution for a linear equation.
  • The process of checking the solution for a linear equation involves substituting the proposed values for the variables back into the original equation. This means taking the values you have determined for the variables and replacing them in the equation to see if the equation is still true. If the equation is true, then the solution is correct. If the equation is not true, then there is an error in the problem-solving process, and you will need to review your work to identify and correct the mistake.
• Analyze the importance of checking the solution when using a general strategy to solve linear equations.
  • Checking the solution is critically important when using a general strategy to solve linear equations because it helps to ensure the accuracy and validity of the final result. By substituting the solution back into the original equation, you can verify that the proposed values for the variables satisfy the equation and that the problem-solving process was carried out correctly. This step allows you to identify any errors or mistakes made during the intermediate steps, such as in the algebraic manipulations or the application of the general problem-solving strategy. Thoroughly checking the solution is essential for building confidence in the final result and ensuring that the linear equation is solved correctly.

Related terms

Substitution:

The act of replacing a variable or expression in an equation with a specific value or expression.

Algebraic Manipulation:

The process of rearranging, simplifying, or transforming an equation or expression using the rules of algebra.

Validation: The confirmation that a solution or result is correct, accurate, and meets the requirements of the original problem.