91Ó°ÊÓ

Variable substitution is a fundamental prealgebra concept that involves replacing a variable with a given numerical value. In our given problem, we have the expression \(-6x - 6\) and we need to evaluate it when \(x = 3\). The first thing we do is substitute 3 for every occurrence of \(x\) in the expression. This is because the variable \(x\) represents a placeholder that can take on different values.

• Identify the variable in your expression, in this case, \(x\).
• Replace the variable with its given value, turning \(-6x - 6\) into \(-6(3) - 6\).

Understanding variable substitution is crucial because it allows us to simplify and ultimately solve expressions.

Expression evaluation refers to the process of calculating the numerical value of an expression after substituting variables with numbers. The main goal is to follow mathematical operations in the correct sequence, often remembered by the PEMDAS/BODMAS rule (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In our expression \(-6(3) - 6\), we first perform the multiplication:

• Multiply \(-6\) by \(3\) to get \(-18\).

After we evaluate the multiplication, we are left with the simpler expression \(-18 - 6\). As you proceed, ensure each step adheres to the operation precedence. This practice ensures accuracy in obtaining the final result.

Basic arithmetic operations are the foundational mathematical operations used throughout prealgebra. They include:

• Addition
• Subtraction
• Multiplication
• Division

In our problem, we used two of these crucial operations: multiplication and subtraction.

Step-by-Step Application

Let's revisit how we handled these operations:

• Multiplication: We multiplied \(-6\) by \(3\) to end up with \(-18\).
• Subtraction: We performed \(-18 - 6\), giving us \(-24\).

Remember that performing accurate basic arithmetic operations is crucial, as they form the building blocks for more complex mathematical concepts and problem-solving.