91Ó°ÊÓ

Substitution in algebra is a method used to replace variables with their corresponding values. It allows us to transform an abstract algebraic expression into a concrete numerical value. In our exercise, we have the expression \(8x - 3\) and we need to evaluate it at \(x = 4\).
By substituting \(x\) with 4, we directly place the given value into the expression. This transformation is straightforward but crucial for solving algebraic problems.
Understanding substitution helps students translate real-world scenarios into solvable math equations. For instance, if a problem mentions the price of 8 items reduced by 3 dollars each, we can model it using algebra and substitute specific values to find the final cost.

Simplifying expressions is the process of making an expression easier to work with. By reducing its complexity, we allow for more effortless calculation and interpretation. In the given example, our expression is \(8x - 3\).
After substituting \(x\) with 4, it changes to \(8(4) - 3\).
At this stage, we simplify step-by-step:

• First, we perform the multiplication: \(8 \times 4 = 32\).
• Then, we handle the subtraction: \(32 - 3 = 29\).

These steps break down the process so we can easily follow and understand the solution. Simplifying expressions helps to prevent errors and clarifies the path to the final answer.

Basic arithmetic operations are foundational skills in mathematics, including addition, subtraction, multiplication, and division. In our exercise, we particularly focus on multiplication and subtraction.
When we substitute \(x = 4\) into \(8x - 3\), we first encounter multiplication: \(8 \times 4\). This yields 32.
Next, we perform subtraction: \(32 - 3\) simplifies to 29.
Mastering these basic operations is essential, as they are the building blocks for more complex math problems. Practicing these operations helps to develop accuracy and speed in calculations, which are beneficial in both academic and real-life scenarios.