91Ó°ÊÓ

Numerical evaluation is a crucial step when solving equations for specific values. It involves substituting the variable with a given number and simplifying to find the result. In this exercise, we have the equation \( t = 21x + 6 \) and need to determine the value of \( t \) when \( x = 97 \).Once the substitution happens, your main task is to perform the multiplication and addition precisely. This step is essential because it bridges the abstract algebraic expression to tangible numbers relating to the problem.Simplifying the expression, we multiply \(21\) and \(97\), then add \(6\) to this product to finally evaluate the numerical value of \( t \). This process requires accuracy to ensure the solution reflects the correct value, which in this case is \( 2043 \). Keeping track of your arithmetic as you numerically evaluate helps ensure you do not lose sight of each step.

Variable substitution is one of the first steps in solving or evaluating an equation. It means to take a known value and replace a variable with it. In our example equation \( t = 21x + 6 \), the task is to find \( t \) for a known \( x \), which is \( 97 \).By substituting \( 97 \) for \( x \), the abstract expression becomes more specific: \( t = 21(97) + 6 \). The substitution step is critical as it allows you to convert the general formula into a specific numeric sequence that you can compute.This concept of variable substitution is foundational to algebra. It serves to simplify expressions, making problem-solving more accessible and allowing for numerical evaluation to solve for the unknowns.

Arithmetic operations form the backbone of evaluating and solving equations. They include basic operations like addition, subtraction, multiplication, and division. In the given problem, after substituting \( x = 97 \) into \( t = 21x + 6 \), arithmetic operations allow us to further simplify \( t = 21 \times 97 + 6 \).First, perform multiplication: \( 21 \times 97 \). It helps to break this down into smaller steps, like calculating \( 21 \times (100 - 3) \) if that simplifies your process. After you find that \( 21 \times 97 = 2037 \), the next step is an addition, \( 2037 + 6 \), to arrive at the result: \( 2043 \).Accuracy in carrying out arithmetic operations is crucial as small errors can lead to incorrect final values. Practicing these operations helps improve speed and precision, which are helpful in both exams and real-life applications.