91Ó°ÊÓ

Variable substitution is the initial step in evaluating algebraic expressions, where we replace each variable with its given numerical value. Imagine you're baking a cake and the recipe calls for labeled ingredients. For this exercise, you have the expression \(5x - y + 4z\), and you need to plug in the specific values: \(x = -2\), \(y = 4\), and \(z = -1\). Picture this as swapping placeholders with actual ingredients for the recipe. Here are the steps to master substitution:

• Identify each variable in the expression.
• Replace each variable with the given numerical value.
• Write the new expression with the numbers replacing the variables.

By substituting \(x = -2\), \(y = 4\), and \(z = -1\) into our expression, we transform it into \(5(-2) - 4 + 4(-1)\). This ensures the expression is ready for the next steps in simplifying and calculating its value.

Once we've substituted the variables, the next step is to simplify the expression. Simplifying means taking complex parts of an expression and making them easier to understand and work with.First, evaluate each separate term within the expression:

• For the term \(5(-2)\), multiply to get \(-10\).
• The term \(-y\) becomes \(-4\), since you substitute \(y = 4\).
• For \(4(-1)\), multiply to find \(-4\).

After evaluating these terms individually, you are left with a simpler numeric expression: \(-10 - 4 - 4\). Breaking down each operation helps avoid errors and confirms that each component of the expression is rightly executed before moving on to combinations or further calculations.

After simplifying, it's time for the final step: evaluating the expression. This is where you bring together all the simplified terms to find the total value.Think of it like tallying up a list of expenses or a scorecard. From the simplified expression \(-10 - 4 - 4\), follow these steps:

• Start by adding or subtracting each number sequentially.
• First, combine \(-10\) and \(-4\) to get \(-14\).
• Then, add \(-4\) to \(-14\) which results in \(-18\).

By conducting these operations one step at a time, we ensure accuracy and clarity in reaching the expression's final value: \(-18\). Evaluating expressions helps us apply real-world values to abstract algebraic equations, making complex math accessible and understandable.