Simplify The Expression:${ -|-58| = \square }$

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Introduction

In mathematics, absolute value equations are a fundamental concept that deals with the distance of a number from zero on the number line. The absolute value of a number is its distance from zero, and it is always non-negative. In this article, we will simplify the expression |-58| and understand the concept of absolute value equations.

What is Absolute Value?

Absolute value is a mathematical operation that returns the distance of a number from zero on the number line. It is denoted by two vertical lines, and it is always non-negative. For example, |-5| = 5, |0| = 0, and |10| = 10. The absolute value of a number is its distance from zero, and it is always positive.

Simplifying the Expression |-58|

To simplify the expression |-58|, we need to find the distance of -58 from zero on the number line. Since -58 is a negative number, we need to take its absolute value to find its distance from zero. The absolute value of -58 is 58, because it is 58 units away from zero on the number line.

Properties of Absolute Value

Absolute value has several properties that are important to understand:

  • The absolute value of a number is always non-negative.
  • The absolute value of a number is its distance from zero on the number line.
  • The absolute value of a negative number is positive.
  • The absolute value of a positive number is positive.

Examples of Absolute Value Equations

Here are some examples of absolute value equations:

  • |-25| = ?
  • |0| = ?
  • |10| = ?
  • |-100| = ?

Solution to the Examples

Here are the solutions to the examples:

  • |-25| = 25
  • |0| = 0
  • |10| = 10
  • |-100| = 100

Conclusion

In conclusion, absolute value equations are an important concept in mathematics that deals with the distance of a number from zero on the number line. The absolute value of a number is its distance from zero, and it is always non-negative. We simplified the expression |-58| and understood the concept of absolute value equations. We also discussed the properties of absolute value and provided examples of absolute value equations.

Frequently Asked Questions

Here are some frequently asked questions about absolute value equations:

  • What is the absolute value of a negative number?
  • What is the absolute value of a positive number?
  • What is the absolute value of zero?
  • How do you simplify an absolute value equation?

Answers to the FAQs

Here are the answers to the FAQs:

  • The absolute value of a negative number is positive.
  • The absolute value of a positive number is positive.
  • The absolute value of zero is zero.
  • To simplify an absolute value equation, you need to find the distance of the number from zero on the number line.

Final Thoughts

In conclusion, absolute value equations are an important concept in mathematics that deals with the distance of a number from zero on the number line. The absolute value of a number is its distance from zero, and it is always non-negative. We simplified the expression |-58| and understood the concept of absolute value equations. We also discussed the properties of absolute value and provided examples of absolute value equations.

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Introduction

In our previous article, we discussed the concept of absolute value equations and how to simplify them. In this article, we will provide a comprehensive Q&A guide to help you understand absolute value equations better.

Q&A: Absolute Value Equations

Q1: What is the absolute value of a negative number?

A1: The absolute value of a negative number is positive. For example, |-5| = 5.

Q2: What is the absolute value of a positive number?

A2: The absolute value of a positive number is positive. For example, |10| = 10.

Q3: What is the absolute value of zero?

A3: The absolute value of zero is zero. |0| = 0.

Q4: How do you simplify an absolute value equation?

A4: To simplify an absolute value equation, you need to find the distance of the number from zero on the number line. For example, |-58| = 58.

Q5: What is the difference between absolute value and distance?

A5: Absolute value and distance are related but not the same. Absolute value is a mathematical operation that returns the distance of a number from zero on the number line, while distance is a measure of how far apart two points are.

Q6: Can you provide examples of absolute value equations?

A6: Yes, here are some examples of absolute value equations:

  • |-25| = ?
  • |0| = ?
  • |10| = ?
  • |-100| = ?

Q7: How do you solve absolute value equations?

A7: To solve absolute value equations, you need to find the value of the expression inside the absolute value bars. For example, |-5| = 5, so the equation |-5| = 3 becomes 5 = 3, which is not true. Therefore, the equation |-5| = 3 has no solution.

Q8: Can you provide examples of absolute value inequalities?

A8: Yes, here are some examples of absolute value inequalities:

  • |-25| < 10
  • |0| > 5
  • |10| < 20
  • |-100| > 50

Q9: How do you solve absolute value inequalities?

A9: To solve absolute value inequalities, you need to find the values of the expression inside the absolute value bars that satisfy the inequality. For example, |-25| < 10 becomes -10 < -25 < 10, which is true. Therefore, the inequality |-25| < 10 has a solution.

Q10: Can you provide examples of real-world applications of absolute value equations?

A10: Yes, here are some examples of real-world applications of absolute value equations:

  • A company has a budget of $100 to spend on advertising. If the cost of advertising is $58, how much money is left over?
  • A person has a bank account with a balance of -$58. If they deposit $100, what is the new balance?
  • A car travels 58 miles in 2 hours. What is the average speed of the car?

Conclusion

In conclusion, absolute value equations are an important concept in mathematics that deals with the distance of a number from zero on the number line. We provided a comprehensive Q&A guide to help you understand absolute value equations better. We discussed the properties of absolute value, how to simplify absolute value equations, and how to solve absolute value inequalities. We also provided examples of real-world applications of absolute value equations.

Final Thoughts

In conclusion, absolute value equations are a fundamental concept in mathematics that deals with the distance of a number from zero on the number line. We hope that this Q&A guide has helped you understand absolute value equations better and provided you with a solid foundation to build upon.