Problem 125 - Prealgebra and Introductory Algebra

Question

Evaluate the expression for the given values of the variables. \(-x-y,\) for \(x=-3\) and \(y=9\)

Step-by-Step Solution

Answer

The evaluated result of the expression \(-x - y\), for \(x = -3\) and \(y = 9\), is \(-6\).

Step 1: Substituting the Variables

The first step involves replacing the variables \(x\) and \(y\) with the given values in the expression \(-x-y\). Hence, for \(x=-3\) and \(y=9\), we substitute these values into the expression to get \(-(-3) - 9\)

Step 2: Simplifying the Expression

In this step, the expression is simplified by resolving the negations. The negative sign before \(-3\) makes it a positive value. Hence the expression becomes \(3 - 9\).

Step 3: Final Calculation

Finally, we perform the remaining operation (subtraction), which gives \(3 - 9 = -6\) as the final result.

Key Concepts

Substitution

Substitution in algebra is the process of replacing variables with specific values to simplify an expression or equation. Think of it as a way of solving a puzzle by filling in the gaps with numbers provided. This makes it easier to work with and ultimately find an answer.

To substitute values into an algebraic expression, simply identify each variable. For example, in the expression

• Replace each appearance of the variable with the given value. This step is crucial as it sets the groundwork for further simplification.
• Always double-check your substituted values; a mistake here can lead to incorrect results in later steps.

In more complex expressions, remain organized and systematically substitute each value, making note of where and what each variable has been replaced with. This will streamline the process of evaluating the expression and ensure accuracy.

Negative Numbers

Working with negative numbers can be a bit tricky, but understanding a few basic rules can make it much easier. When you see a negative sign, it indicates the opposite of a positive value. In other words,

• Two negatives make a positive: When two negative signs appear together, they cancel each other out. This is seen in the expression
• Adding a negative is the same as subtracting the positive: For example, subtracting a positive number such as 9 from a positive one is the same as adding a negative number, meaning 3 - 9 equals 3 + (-9).

Understanding how to manipulate these numbers is essential to solving algebraic expressions effectively. Being cautious with the placement and interpretation of negative signs will help avoid common calculation errors.

Algebraic Expressions

An algebraic expression is a combination of numbers, variables, and operations (like addition or subtraction). Understanding these can help solve real-world problems more effectively. They are the building blocks of algebra and need to be decoded through careful substitution and arithmetic. Basics of Algebraic Expressions:

• Variables represent unknown values and are usually represented by letters such as x or y.
• Coefficients are the numbers alongside variables, showing how many of the variable are present.
• Operations dictate how the different parts of the expression interact with each other.

By substituting specific values into these expressions, one can simplfy them into a single numerical answer, just as in the original exercise. Algebraic expressions are a foundational element of math and science, helping to express and solve real-world problems.