Evaluate/Simplify The Expression. − 2 ∣ X + Y ∣ -2|x+y| − 2∣ X + Y ∣ Evaluate The Expression Above When X = 10 X = 10 X = 10 And Y = − 2 Y = -2 Y = − 2 . Answer: \qquad

Mar 12, 2025 by ADMIN 169 views

Evaluate the Expression: Simplifying $-2|x+y|$

Introduction

In this article, we will delve into the world of mathematical expressions and learn how to simplify the given expression $-2|x+y|$ . We will also evaluate this expression when $x = 10$ and $y = -2$ . The expression involves absolute value, which can sometimes be tricky to work with. However, with a clear understanding of the concept and some simple algebraic manipulations, we can simplify the expression and find its value.

Understanding Absolute Value

Before we dive into the expression, let's take a moment to understand what absolute value is. The absolute value of a number $a$ , denoted by $|a|$ , is the distance of $a$ from zero on the number line. In other words, it is the magnitude of $a$ without considering its direction. For example, the absolute value of $-3$ is $3$ , and the absolute value of $4$ is also $4$ . This means that the absolute value of any number is always non-negative.

Simplifying the Expression

Now that we have a good understanding of absolute value, let's simplify the expression $-2|x+y|$ . To do this, we need to follow the order of operations (PEMDAS):

Evaluate the expression inside the absolute value signs: $x+y$
Take the absolute value of the result: $|x+y|$
Multiply the result by $-2$ : $-2|x+y|$

Let's start by evaluating the expression inside the absolute value signs: $x+y$ . We are given that $x = 10$ and $y = -2$ , so we can substitute these values into the expression:

$x+y = 10 + (-2) = 8$

Now that we have the value of $x+y$ , we can take its absolute value:

$|x+y| = |8| = 8$

Finally, we multiply the result by $-2$ :

$-2|x+y| = -2(8) = -16$

Conclusion

In this article, we simplified the expression $-2|x+y|$ by following the order of operations and using the concept of absolute value. We also evaluated this expression when $x = 10$ and $y = -2$ , and found that the result is $-16$ . This demonstrates the importance of understanding absolute value and how to work with it in mathematical expressions.

Frequently Asked Questions

What is the absolute value of a number? The absolute value of a number $a$ is the distance of $a$ from zero on the number line, denoted by $|a|$ .
How do I simplify an expression involving absolute value? To simplify an expression involving absolute value, follow the order of operations (PEMDAS) and evaluate the expression inside the absolute value signs first.
What is the value of $-2|x+y|$ when $x = 10$ and $y = -2$ ? The value of $-2|x+y|$ when $x = 10$ and $y = -2$ is $-16$ .

Additional Resources

Khan Academy: Absolute Value
Mathway: Absolute Value
Wolfram Alpha: Absolute Value

Final Thoughts

Simplifying expressions involving absolute value can be a bit tricky, but with practice and patience, you can master this concept. Remember to follow the order of operations and evaluate the expression inside the absolute value signs first. With this article, you should now have a better understanding of how to simplify the expression $-2|x+y|$ and evaluate it when given specific values for $x$ and $y$ .

Introduction

In our previous article, we explored the concept of absolute value and how to simplify expressions involving it. We also evaluated the expression $-2|x+y|$ when $x = 10$ and $y = -2$ . In this article, we will answer some frequently asked questions about simplifying expressions involving absolute value.

Q&A

Q: What is the absolute value of a negative number?

A: The absolute value of a negative number is always positive. For example, the absolute value of $-3$ is $3$ , and the absolute value of $-4$ is $4$ .

Q: How do I simplify an expression involving absolute value when the expression inside the absolute value signs is negative?

A: When the expression inside the absolute value signs is negative, you can simplify the expression by multiplying the absolute value by $-1$ . For example, if you have the expression $|x-5|$ , and you know that $x < 5$ , you can simplify the expression by multiplying the absolute value by $-1$ : $-(x-5)$ .

Q: Can I simplify an expression involving absolute value by combining like terms?

A: Yes, you can simplify an expression involving absolute value by combining like terms. For example, if you have the expression $|x+3| + |x-2|$ , you can combine the like terms by adding the absolute values: $|x+3| + |x-2| = |x+3+x-2| = |2x+1|$ .

Q: How do I evaluate an expression involving absolute value when the expression inside the absolute value signs is a variable?

A: When the expression inside the absolute value signs is a variable, you can evaluate the expression by considering the possible values of the variable. For example, if you have the expression $|x+2|$ , and you know that $x$ can be either positive or negative, you can evaluate the expression by considering the possible values of $x$ : $|x+2| = x+2$ if $x \geq -2$ , and $|x+2| = -(x+2)$ if $x < -2$ .

Q: Can I simplify an expression involving absolute value by using algebraic manipulations?

A: Yes, you can simplify an expression involving absolute value by using algebraic manipulations. For example, if you have the expression $|x^2-4|$ , you can simplify the expression by factoring the quadratic expression: $|x^2-4| = |(x-2)(x+2)| = |x-2||x+2|$ .

Q: How do I determine the value of an expression involving absolute value when the expression inside the absolute value signs is a function?

A: When the expression inside the absolute value signs is a function, you can determine the value of the expression by evaluating the function at the given input. For example, if you have the expression $|f(x)|$ , and you know that $f(x) = x^2-4$ , you can determine the value of the expression by evaluating the function at the given input: $|f(x)| = |x^2-4|$ .

Conclusion

In this article, we answered some frequently asked questions about simplifying expressions involving absolute value. We covered topics such as the absolute value of negative numbers, simplifying expressions involving absolute value when the expression inside the absolute value signs is negative, combining like terms, evaluating expressions involving absolute value when the expression inside the absolute value signs is a variable, and using algebraic manipulations to simplify expressions involving absolute value.

Frequently Asked Questions

What is the absolute value of a negative number? The absolute value of a negative number is always positive.
How do I simplify an expression involving absolute value when the expression inside the absolute value signs is negative? You can simplify the expression by multiplying the absolute value by $-1$ .
Can I simplify an expression involving absolute value by combining like terms? Yes, you can simplify an expression involving absolute value by combining like terms.
How do I evaluate an expression involving absolute value when the expression inside the absolute value signs is a variable? You can evaluate the expression by considering the possible values of the variable.
Can I simplify an expression involving absolute value by using algebraic manipulations? Yes, you can simplify an expression involving absolute value by using algebraic manipulations.

Additional Resources

Khan Academy: Absolute Value
Mathway: Absolute Value
Wolfram Alpha: Absolute Value

Final Thoughts

Simplifying expressions involving absolute value can be a bit tricky, but with practice and patience, you can master this concept. Remember to follow the order of operations and evaluate the expression inside the absolute value signs first. With this article, you should now have a better understanding of how to simplify expressions involving absolute value and answer some frequently asked questions about this topic.