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The substitution method is a powerful technique often used in evaluating polynomials. It involves replacing a variable in an expression with a specific value. In our example, we are substituting the variable \(x\) with the number 2. This is straightforward in our polynomial \(-5x - 6\). You simply take out \(x\), popping a 2 in its place, so it transforms into \(-5(2) - 6\).
This technique ensures clarity as it removes the variable from the equation, leaving it with simple numbers to handle.

• Identify the variable: You're looking for where \(x\), or any letter, appears in the equation.
• Swap it out: Insert the given number or value in place of the variable.

Using substitution is like replacing a missing puzzle piece with exactly the piece you need, making the problem much simpler to solve.

Arithmetic operations are basic mathematical tasks: addition, subtraction, multiplication, and division. They are the building blocks for evaluating any equation or expression.
Once we substitute 2 for \(x\) in the polynomial \(-5x - 6\), we switch gears to multiplication first because of the order of operations (often remembered by PEMDAS or BIDMAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
So, we multiply \(-5\) and \(2\), resulting in \(-10\).
This gives us: \(-10 - 6\). Now, we need to carry out the subtraction operation.
Here's how you deal with arithmetic operations step by step:

• Perform any multiplication or division first.
• Move on to addition or subtraction.

These steps will organize your calculations and help ensure that each action takes place in the correct sequence, leading smoothly to the next phase of problem-solving.

Simplifying expressions means making them as straightforward as possible. It's the final step in many math problems after you've completed all your arithmetic operations. The goal is to present the polynomial or expression in its simplest form.
After multiplying in our equation, we were left with \(-10 - 6\). The only job left is to subtract 6 from \(-10\). This operation merges everything into a single number: \(-16\).
When simplifying expressions, follow these tips:

• Combine like terms if there are any. Like terms have the same variable parts, but in this case, we just have plain numbers.
• Be careful with negative numbers; they follow their own rules, especially in subtraction.

Simplification shows the final, neat form of your work. It ensures that when you present your answer, it's easy to understand and completely resolves the initial equation.