Select The Correct Answer.Evaluate The Following Expression When X = − 5 X = -5 X = − 5 And Y = 25 Y = 25 Y = 25 : 5 ∣ X ∣ − Y 3 X \frac{5|x| - Y^3}{x} X 5∣ X ∣ − Y 3 ​ A. -630 B. 3,120 C. 620 D. -3,130

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Introduction

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When evaluating mathematical expressions, it's essential to understand the rules and properties of absolute values and exponents. In this article, we will focus on evaluating the expression $\frac{5|x| - y^3}{x}$ when $x = -5$ and $y = 25$. We will break down the expression step by step, applying the rules of absolute values and exponents to arrive at the correct answer.

Understanding Absolute Values

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Absolute values are a fundamental concept in mathematics, representing the distance of a number from zero on the number line. The absolute value of a number $x$, denoted by $|x|$, is defined as:

$$|x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}$$

In the given expression, we have $|x|$, which means we need to consider the absolute value of $x$ when evaluating the expression.

Evaluating the Expression

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Let's start by substituting the given values of $x$ and $y$ into the expression:

$$\frac{5|x| - y^3}{x} = \frac{5|-5| - 25^3}{-5}$$

Now, let's evaluate the absolute value of $x$:

$$|-5| = 5$$

So, the expression becomes:

$$\frac{5(5) - 25^3}{-5} = \frac{25 - 15625}{-5}$$

Next, let's evaluate the exponent $25^3$:

$$25^3 = 15625$$

Now, we can simplify the expression:

$$\frac{25 - 15625}{-5} = \frac{-15600}{-5}$$

Simplifying the Expression

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To simplify the expression, we can divide the numerator by the denominator:

$$\frac{-15600}{-5} = 3120$$

Therefore, the correct answer is:

B. 3,120

Conclusion

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Evaluating expressions with absolute values and exponents requires a clear understanding of the rules and properties involved. By breaking down the expression step by step and applying the rules of absolute values and exponents, we can arrive at the correct answer. In this article, we evaluated the expression $\frac{5|x| - y^3}{x}$ when $x = -5$ and $y = 25$ and found that the correct answer is B. 3,120.

Frequently Asked Questions

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Q: What is the absolute value of a number?

A: The absolute value of a number $x$, denoted by $|x|$, is defined as the distance of $x$ from zero on the number line.

Q: How do I evaluate an expression with an absolute value?

A: To evaluate an expression with an absolute value, you need to consider the absolute value of the variable involved. If the variable is positive, the absolute value is the same as the variable. If the variable is negative, the absolute value is the opposite of the variable.

Q: What is the exponent of a number?

A: The exponent of a number is the power to which the number is raised. For example, $25^3$ means $25$ raised to the power of $3$.

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, you can divide the numerator by the denominator.

Additional Resources

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• Absolute Value
• Exponents
• Fractions

Related Articles

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• Evaluating Expressions with Variables
• Simplifying Fractions
• Understanding Absolute Values
  

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Introduction

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In our previous article, we evaluated the expression $\frac{5|x| - y^3}{x}$ when $x = -5$ and $y = 25$ and found that the correct answer is B. 3,120. In this article, we will answer some frequently asked questions related to evaluating expressions with absolute values and exponents.

Q&A

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Q: What is the absolute value of a number?

A: The absolute value of a number $x$, denoted by $|x|$, is defined as the distance of $x$ from zero on the number line.

Q: How do I evaluate an expression with an absolute value?

A: To evaluate an expression with an absolute value, you need to consider the absolute value of the variable involved. If the variable is positive, the absolute value is the same as the variable. If the variable is negative, the absolute value is the opposite of the variable.

Q: What is the exponent of a number?

A: The exponent of a number is the power to which the number is raised. For example, $25^3$ means $25$ raised to the power of $3$.

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, you can divide the numerator by the denominator.

Q: What is the difference between an absolute value and a negative number?

A: An absolute value is the distance of a number from zero on the number line, while a negative number is a number that is less than zero. For example, $|-5| = 5$ is the absolute value of $-5$, while $-5$ is a negative number.

Q: Can I simplify an expression with an absolute value and an exponent?

A: Yes, you can simplify an expression with an absolute value and an exponent by following the order of operations (PEMDAS). First, evaluate the exponent, then the absolute value, and finally the expression.

Q: How do I evaluate an expression with multiple absolute values?

A: To evaluate an expression with multiple absolute values, you need to consider the absolute value of each variable involved. If the variable is positive, the absolute value is the same as the variable. If the variable is negative, the absolute value is the opposite of the variable.

Q: Can I use a calculator to evaluate an expression with absolute values and exponents?

A: Yes, you can use a calculator to evaluate an expression with absolute values and exponents. However, make sure to follow the order of operations (PEMDAS) and use the correct buttons on the calculator.

Examples

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Example 1: Evaluating an expression with an absolute value and an exponent

Evaluate the expression $\frac{5|x| - y^3}{x}$ when $x = -5$ and $y = 25$.

Solution:

$$\frac{5|x| - y^3}{x} = \frac{5|-5| - 25^3}{-5} = \frac{25 - 15625}{-5} = \frac{-15600}{-5} = 3120$$

Example 2: Evaluating an expression with multiple absolute values

Evaluate the expression $\frac{|x| + |y|}{x}$ when $x = -5$ and $y = -3$.

Solution:

$$\frac{|x| + |y|}{x} = \frac{|-5| + |-3|}{-5} = \frac{5 + 3}{-5} = \frac{8}{-5} = -\frac{8}{5}$$

Conclusion

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Evaluating expressions with absolute values and exponents requires a clear understanding of the rules and properties involved. By following the order of operations (PEMDAS) and considering the absolute value of each variable involved, you can simplify expressions with absolute values and exponents. In this article, we answered some frequently asked questions related to evaluating expressions with absolute values and exponents.

Frequently Asked Questions

---

Q: What is the absolute value of a number?

A: The absolute value of a number $x$, denoted by $|x|$, is defined as the distance of $x$ from zero on the number line.

Q: How do I evaluate an expression with an absolute value?

A: To evaluate an expression with an absolute value, you need to consider the absolute value of the variable involved. If the variable is positive, the absolute value is the same as the variable. If the variable is negative, the absolute value is the opposite of the variable.

Q: What is the exponent of a number?

A: The exponent of a number is the power to which the number is raised. For example, $25^3$ means $25$ raised to the power of $3$.

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, you can divide the numerator by the denominator.

Additional Resources

---

• Absolute Value
• Exponents
• Fractions

Related Articles

---

• Evaluating Expressions with Variables
• Simplifying Fractions
• Understanding Absolute Values