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Substitution in Algebra involves replacing a variable in an expression or equation with a specific value. This is a technique used when we're given a particular number for a variable and need to find out what the expression equals when that variable is replaced.
In the given exercise, we have the expression \(-2 - 2x\). When we substitute \(x = -3\) into this expression, we replace every instance of \(x\) with \(-3\). This changes the original expression to \(-2 - 2(-3)\).
Substitution allows us to convert a general algebraic expression into a specific arithmetic expression, which can then be evaluated using basic operations.

Evaluating expressions is the process of determining the value of an expression once the variables have been substituted with their values. After substitution, we proceed to evaluate or simplify the expression to find a numerical value.
In our example, once we substitute \(-3\) for \(x\), the expression \(-2 - 2(-3)\) needs to be evaluated. We start by solving any multiplications or divisions: \(-2 \cdot -3 = 6\). This changes our expression to \(-2 + 6\).
The final step in evaluating the expression is to perform the remaining basic arithmetic operations. In this case, that involves summing \(-2\) and \(6\), resulting in \(4\). Always remember to follow the correct order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often abbreviated as PEMDAS.

Basic arithmetic operations are essential building blocks in math. They include addition, subtraction, multiplication, and division. In evaluating expressions after substitution, you'll often need to use these operations.
Let's break down their use in our problem:

• Multiplication: After substitution, we needed to multiply the terms \(-2\) and \(-3\). Remember, multiplying two negative numbers results in a positive number, hence \(-2 \times -3 = 6\).
• Addition/Subtraction: Finally, we treat the addition and subtraction operations as they are. Once reduced, our expression became \(-2 + 6\), which simplifies to the number \(4\).

Being comfortable with these basic operations ensures efficiency and accuracy when solving algebraic expressions. Mastering these foundational skills is critical for more advanced topics like algebra and calculus.