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Evaluating algebraic expressions means finding the value of the expression given specific values for its variables. In our example, we want to evaluate the expression \(-5x + 6\) when \(x = -3\). This involves substituting the specified value of \(x\) into the expression. When we plug \(-3\) in place of \(x\), the expression becomes \(-5(-3) + 6\). The process is like solving a puzzle, where you replace variables with numbers, transforming the expression into a single numerical value.
When you substitute the value into the expression, be careful with the signs, especially if you're dealing with negative numbers. Every step alters the expression, moving it closer to the final numeric solution. This skill is essential in algebra as it allows you to find concrete answers from abstract formulas.

Negative numbers can be a bit tricky, but understanding them is crucial when evaluating expressions. A negative number is simply a number less than zero, indicated by a minus sign (\(-\)). When multiplying two negative numbers, the result is positive. This might seem surprising, but you can think of it in reverse terms: a negative times a negative pushes the value back into positive territory.
- Multiplying a negative number by another negative number gives a positive result (\(-5 \times -3 = 15\)).- When adding and subtracting negative numbers, pay close attention to the signs. For instance, adding a negative number to a positive number lowers the overall amount.
This understanding clears up a lot of confusion and is vital for correctly solving algebraic expressions.

Order of operations is a fundamental principle that dictates the correct sequence to solve parts of a mathematical expression. This sequence is crucial to ensure everyone gets the same result when evaluating an expression. Remember the acronym PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)

In our example \(-5(-3) + 6\), after substituting the value of \(x\), we first handled the multiplication \((-5 \times -3)\) before performing the addition \((+6)\). This guarantees that each operation is executed in the right order, leading us to the correct result.
Always following the order of operations ensures accurate solutions regardless of the complexity of the expression. By consistently applying this method, calculations become predictable and reliable.