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Substitution is a fundamental technique in algebra where we replace variables with their corresponding values. In the context of evaluating expressions, substitution simplifies solving by converting an algebraic expression into a more straightforward arithmetic problem.

For example, consider the expression \(a+4)-8\) when \(a=7\). Substitution involves taking the given value of \(a\) and replacing the variable with that number. Here's how it works:

• Identify the variable in the expression, which is \(a\) in this case.
• Replace \(a\) with its given value, so the expression becomes \((7+4)-8\).

By substituting \(7\) for \(a\), we transform the algebraic expression into a simple arithmetic operation, paving the way for an easier path to reach the solution.

In algebra, operations include addition, subtraction, multiplication, and division, which are used to manipulate algebraic expressions and equations. The order in which these operations are performed is crucial, and we follow the orders of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

In the given example, after substituting \(7\) for \(a\), we carry out the operations as follows:

• The expression inside the parentheses \(7+4\) is addressed first, emphasizing the 'P' in PEMDAS.
• We add the numbers inside the parentheses to get \(11\).
• Finally, we subtract \(8\) from the sum we obtained, following the order of operations to get the solution \(3\).

Understanding the correct sequence of operations allows us to accurately evaluate algebraic expressions.

Expressions and equations are integral parts of algebra that represent mathematical relationships. An expression is a combination of numbers, variables, and operation symbols that stands for a particular quantity. Unlike an equation, it does not have an equality sign \(=\); therefore, it cannot be solved but can be simplified or evaluated for given values.

An equation, on the other hand, is a statement that two expressions are equal, featuring an equality sign. To solve an equation, we find the values of the variables that make the equation true.

In the exercise \(a+4)-8\), we are dealing with an expression, not an equation. To evaluate this expression for \(a=7\), we don't solve for \(a\); instead, we simplify the expression by substituting and performing operations to find the numerical value that the expression represents.