Evaluate: -415|x|+y For X=-1, Y=150

Have you ever encountered an expression and felt a bit puzzled about how to solve it? Don't worry, you're not alone! Evaluating expressions is a fundamental skill in mathematics, and once you grasp the basics, it becomes much easier. In this article, we'll break down the process of evaluating the expression $-415|x|+y$ when $x = -1$ and $y = 150$. So, let's dive in and make math a little less mysterious!

Understanding the Expression

Before we start plugging in numbers, let's take a closer look at the expression we're dealing with: $-415|x|+y$. This expression involves a few key components:

• Variables: $x$ and $y$ are variables, which means they represent unknown values. In this case, we're given specific values for $x$ and $y$.
• Absolute Value: The vertical bars $|x|$ represent the absolute value of $x$. The absolute value of a number is its distance from zero, so it's always non-negative. For example, $|-3| = 3$ and $|3| = 3$.
• Multiplication: The term $-415|x|$ indicates that we need to multiply $-415$ by the absolute value of $x$.
• Addition: Finally, we add the result of the multiplication to the value of $y$.

Understanding each component is crucial for correctly evaluating the expression. This expression combines multiplication, addition, and absolute value, making it a good example for practicing order of operations. We will need to substitute the given values for x and y and simplify. Remember, absolute value makes any number inside it non-negative. Let’s break it down step by step to make sure we understand each operation clearly.

Step 1: Substitute the Values

The first step in evaluating the expression is to substitute the given values for the variables. We're given that $x = -1$ and $y = 150$. So, we replace $x$ with $-1$ and $y$ with $150$ in the expression:

$-415|-1|+150$

Now, we have an expression with only numbers and operations, which we can simplify.

Substitution is a fundamental step in algebra, allowing us to move from abstract expressions to concrete numerical values. This step transforms the expression into a form we can directly calculate. By replacing variables with their assigned values, we set the stage for the arithmetic operations that will lead us to the final answer. In this case, we are substituting $x$ with $-1$ and $y$ with $150$, which lays the groundwork for the subsequent steps in the evaluation process. It’s like setting up the pieces on a chessboard before making your moves. The accuracy of this initial substitution is crucial because any error here will propagate through the rest of the calculation, leading to an incorrect result. Therefore, double-checking the substitution ensures a solid foundation for solving the problem.

Step 2: Evaluate the Absolute Value

Next, we need to evaluate the absolute value. The absolute value of $-1$ is the distance of $-1$ from zero, which is $1$. So, we replace $|-1|$ with $1$:

$-415(1)+150$

Now, the expression looks simpler, and we can move on to the multiplication.

The absolute value function is a core concept in mathematics, converting any number into its non-negative magnitude. In this specific problem, finding the absolute value of $-1$ is a pivotal step because it simplifies the expression and prepares it for further calculations. The absolute value essentially strips away the sign of the number, focusing solely on its distance from zero. This transformation is crucial in various mathematical contexts, including geometry, calculus, and complex analysis. Understanding how absolute value works not only helps in solving this particular expression but also builds a stronger foundation for tackling more complex mathematical problems in the future. It’s like understanding the rules of the game before you start playing; knowing the absolute value concept makes the entire process smoother and more efficient.

Step 3: Perform the Multiplication

Now, we perform the multiplication: $-415$ multiplied by $1$ is $-415$. So, we have:

$-415+150$

We're getting closer to the final answer!

Multiplication is a fundamental arithmetic operation, and in this context, it directly influences the outcome of the expression. Multiplying $-415$ by $1$ might seem straightforward, but it’s a crucial step in preserving the value and sign of the number. Accurate multiplication is essential because it sets the stage for the final addition, where we will combine this product with another value. This step showcases the importance of paying close attention to signs in mathematical operations, as a small error here can lead to a significantly different result. Mastering multiplication is not just about getting the right number; it's about understanding how different operations interact within an expression to produce the correct solution. It's a building block in the broader landscape of mathematical calculations, and proficiency in it is key to solving more complex problems.

Step 4: Perform the Addition

Finally, we perform the addition: $-415$ plus $150$ is $-265$. So, the value of the expression is:

$-265$

And that's it! We've successfully evaluated the expression.

Addition, in this final step, brings together the results of the previous operations, culminating in the final answer. Adding $-415$ and $150$ requires a clear understanding of how to combine numbers with different signs, a basic yet essential skill in arithmetic. This operation isn't just about summing two numbers; it’s about understanding the interplay between positive and negative values and how they contribute to the overall result. The accuracy of this step is paramount because it directly translates to the solution of the expression. It's the last piece of the puzzle, and getting it right validates all the steps that came before. By correctly performing the addition, we confirm our understanding of the order of operations and our ability to apply mathematical principles to solve real problems.

Conclusion

Evaluating expressions might seem daunting at first, but by breaking it down into smaller steps, it becomes much more manageable. Remember to substitute the values, evaluate absolute values, perform multiplication, and then perform addition. With practice, you'll become more confident in your ability to evaluate all sorts of expressions. Keep practicing, and you'll be a math whiz in no time!

To further enhance your understanding of evaluating expressions, you might find resources like Khan Academy's algebra section incredibly helpful. Check it out here: Khan Academy Algebra