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The substitution method is a fundamental concept in algebra that involves replacing variables with their corresponding values. When an expression contains a variable, such as x, it is often given a specific value that it represents. For instance, you may encounter a problem where you need to evaluate the expression 3x + 2 for x = -4.

The process starts by identifying the variable in the expression, which in this case is x, and then replacing it with the given value. Once you substitute -4 for x, the expression transforms into 3(-4) + 2. This new form of the expression can now be simplified using arithmetic operations without the variable, making it easier to calculate the final result.

Understanding the order of operations is crucial when simplifying expressions in mathematics. This set of rules, often remembered by the acronym PEMDAS or BODMAS, guides us through which calculations to perform first in an expression. It stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In our example 3(-4) + 2, we must first tackle the multiplication operation 3 * -4. According to the order of operations, multiplication comes before addition, so we perform this step yielding -12. The expression is now reduced to -12 + 2, and the last step is to add the two numbers together, giving us the simplified result of -10.

Simplifying expressions is the act of reducing an algebraic expression to its simplest form, meaning it can't be broken down any further using the basic operations of arithmetic. The simplified version is easier to understand and work with, especially when solving equations or evaluating algebraic expressions.

In order to simplify an expression like 3(-4) + 2, the substitution has already been made, and then the order of operations is applied. The multiplication 3 * -4 is calculated first, resulting in -12. Following this, we add 2, which leaves us with the final answer -10. The expression has been simplified because it is now a single number and no further operations can be performed.