Select The Expression That Is Equivalent To $|4-3|$.A. 1 B. $\sqrt{7}$ C. $5i$ D. 5

In mathematics, absolute value is a fundamental concept that deals with the magnitude or size of a number, without considering its sign. It is denoted by two vertical lines on either side of the number, like this: $|x|$. When we have an expression inside the absolute value signs, we need to find its equivalent value, which is either positive or zero.

The Given Expression: $|4-3|$

The given expression is $|4-3|$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Subtract 3 from 4: $4-3=1$
2. Take the absolute value of the result: $|1|=1$

Therefore, the equivalent expression to $|4-3|$ is simply 1.

Comparing with the Options

Now, let's compare our result with the given options:

A. 1 B. $\sqrt{7}$ C. $5i$ D. 5

As we can see, option A is the correct answer, which is 1.

Why Not the Other Options?

Let's analyze why the other options are not correct:

• Option B, $\sqrt{7}$, is the square root of 7, which is not related to the absolute value of $4-3$.
• Option C, $5i$, is an imaginary number, which is not relevant to the given expression.
• Option D, 5, is a positive number, but it is not the equivalent value of $|4-3|$.

Conclusion

In conclusion, the equivalent expression to $|4-3|$ is simply 1. This is because the absolute value of a number is its magnitude or size, without considering its sign. By following the order of operations and understanding the concept of absolute value, we can easily evaluate expressions like this one.

Absolute Value: A Brief Overview

Before we move on to more complex expressions, let's take a brief look at the concept of absolute value:

• The absolute value of a number is its distance from zero on the number line.
• It is always non-negative, i.e., greater than or equal to zero.
• The absolute value of a number can be positive or zero, but never negative.

Examples of Absolute Value Expressions

Here are a few more examples of absolute value expressions:

• $|2+3|=5$
• $|-5|=5$
• $|0|=0$

In each of these examples, we need to follow the order of operations and evaluate the expression inside the absolute value signs.

Simplifying Absolute Value Expressions

When simplifying absolute value expressions, we need to consider the following rules:

• If the expression inside the absolute value signs is positive, the absolute value is equal to the expression itself.
• If the expression inside the absolute value signs is negative, the absolute value is equal to the negation of the expression.

Real-World Applications of Absolute Value

Absolute value has many real-world applications, such as:

• Measuring distances: In navigation, absolute value is used to measure distances between two points.
• Calculating errors: In statistics, absolute value is used to calculate the magnitude of errors.
• Modeling physical systems: In physics, absolute value is used to model the behavior of physical systems.

Conclusion

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In our previous article, we explored the concept of absolute value and how to evaluate expressions like $|4-3|$. In this article, we'll answer some frequently asked questions about absolute value to help you better understand this fundamental concept.

Q: What is absolute value?

A: Absolute value is a mathematical concept that deals with the magnitude or size of a number, without considering its sign. It is denoted by two vertical lines on either side of the number, like this: $|x|$.

Q: How do I evaluate an absolute value expression?

A: To evaluate an absolute value expression, you need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the absolute value signs.
2. Take the absolute value of the result.

Q: What is the difference between absolute value and absolute magnitude?

A: Absolute value and absolute magnitude are often used interchangeably, but they have slightly different meanings. Absolute value refers to the magnitude or size of a number, while absolute magnitude refers to the magnitude of a quantity, such as a vector or a complex number.

Q: Can absolute value be negative?

A: No, absolute value cannot be negative. By definition, absolute value is always non-negative, i.e., greater than or equal to zero.

Q: How do I simplify absolute value expressions?

A: To simplify absolute value expressions, you need to consider the following rules:

• If the expression inside the absolute value signs is positive, the absolute value is equal to the expression itself.
• If the expression inside the absolute value signs is negative, the absolute value is equal to the negation of the expression.

Q: What are some real-world applications of absolute value?

A: Absolute value has many real-world applications, such as:

• Measuring distances: In navigation, absolute value is used to measure distances between two points.
• Calculating errors: In statistics, absolute value is used to calculate the magnitude of errors.
• Modeling physical systems: In physics, absolute value is used to model the behavior of physical systems.

Q: Can I use absolute value with complex numbers?

A: Yes, you can use absolute value with complex numbers. The absolute value of a complex number is its magnitude or size, without considering its sign.

Q: How do I find the absolute value of a complex number?

A: To find the absolute value of a complex number, you need to use the formula:

$|a+bi| = \sqrt{a^2 + b^2}$

where $a$ and $b$ are the real and imaginary parts of the complex number, respectively.

Q: What is the absolute value of a vector?

A: The absolute value of a vector is its magnitude or size, without considering its direction. It is denoted by the symbol $||\vec{v}||$.

Q: How do I find the absolute value of a vector?

A: To find the absolute value of a vector, you need to use the formula:

$||\vec{v}|| = \sqrt{x^2 + y^2 + z^2}$

where $x$, $y$, and $z$ are the components of the vector, respectively.

Conclusion

In conclusion, absolute value is a fundamental concept in mathematics that deals with the magnitude or size of a number. By understanding the concept of absolute value and following the order of operations, you can easily evaluate expressions and simplify absolute value expressions. We hope this Q&A guide has helped you better understand absolute value and its applications.