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Understanding the substitution method in algebra is vital for evaluating expressions correctly. This method involves replacing a variable in an expression with a specific value that is given or known. In the context of an exercise like the one provided, where we have the expression \(x+5\) and are told that \(x=2\), the substitution method is our go-to tool.

Think of it as a sort of algebraic 'find and replace', where every instance of \(x\) in the expression gets replaced with 2. The precise steps to follow are simple: first identify the value that the variable represents, and then replace that variable with its given value in the expression. By doing this, you transform an abstract algebraic expression into a simple arithmetic problem that can easily be solved. Remember to always replace the variable with the given value before attempting to solve the expression.

Variable expressions are algebraic statements that contain symbols, usually letters, which represent numbers. In algebra, these variables can be unpredictable and can change depending on the situation or problem. For example, in the expression \(x+5\), \(x\) is the variable because it can represent any number.

In the realm of mathematics, it is critical to understand not only what variable expressions are but also how they function. They are the core of algebra and allow us to construct general formulas and solve problems given specific situations. Knowing how to work with these expressions means you can handle more complex equations and real-world problems that don't always have fixed values.

Solving expressions is the final step in the algebraic journey after the substitution method has been applied. After you've replaced all variables with their respective values, you're left with an arithmetic problem. In the exercise example, after substituting 2 for \(x\), we move from \(x+5\) to \(2+5\).

Solving an expression requires proper order of operations - sometimes represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Fortunately, our example is straightforward, involving only addition. The result of the calculation, \(2+5\), gives us 7, which is the evaluated expression. Being adept at solving expressions not only helps with algebra but sharpens problem-solving skills for a wide range of mathematical tasks.