Jamaal Is Allowed To Walk No Farther Than Three Blocks In Either Direction From The 57th Block Of The Town. Which Absolute Value Equation Can Be Used To Represent Jamaal's Allowed Walking Distance?A. $|x-57|=0$B. $|57-3|=x$C.

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Jamaal is allowed to walk no farther than three blocks in either direction from the 57th block of the town. This means that he can walk up to three blocks north or south of the 57th block. To represent this allowed walking distance using an absolute value equation, we need to consider the distance Jamaal can walk in both directions.

Representing Jamaal's Walking Distance

Let's assume that the distance Jamaal walks from the 57th block is represented by the variable x. Since he can walk up to three blocks in either direction, we can represent this as an absolute value equation.

The absolute value equation |x - 57| = 3 represents the distance Jamaal can walk from the 57th block. This equation states that the absolute value of the difference between x and 57 is equal to 3.

Breaking Down the Equation

Let's break down the equation |x - 57| = 3 to understand it better.

  • The absolute value of a quantity is its distance from zero on the number line.
  • The expression x - 57 represents the distance between x and 57 on the number line.
  • The absolute value of x - 57 is equal to 3, which means that the distance between x and 57 is 3 units.

Solving the Equation

To solve the equation |x - 57| = 3, we need to find the values of x that satisfy the equation.

  • If x - 57 = 3, then x = 60.
  • If x - 57 = -3, then x = 54.

Therefore, the values of x that satisfy the equation |x - 57| = 3 are x = 60 and x = 54.

Conclusion

In conclusion, the absolute value equation that can be used to represent Jamaal's allowed walking distance is |x - 57| = 3. This equation represents the distance Jamaal can walk from the 57th block in both directions.

Answer

The correct answer is A. |x-57|=3.

Discussion

This problem requires an understanding of absolute value equations and how they can be used to represent real-world situations. The equation |x - 57| = 3 represents the distance Jamaal can walk from the 57th block, and it can be used to find the values of x that satisfy the equation.

Additional Examples

Here are some additional examples of absolute value equations that can be used to represent real-world situations:

  • |x - 10| = 2 represents the distance between x and 10 on the number line.
  • |x + 5| = 1 represents the distance between x and -5 on the number line.
  • |x - 20| = 4 represents the distance between x and 20 on the number line.

These examples demonstrate how absolute value equations can be used to represent real-world situations and solve problems.

Conclusion

Q&A: Absolute Value Equations

In this article, we will explore the concept of absolute value equations and provide answers to frequently asked questions about this topic.

Q: What is an absolute value equation?

A: An absolute value equation is an equation that involves the absolute value of a quantity. The absolute value of a quantity is its distance from zero on the number line.

Q: How do I write an absolute value equation?

A: To write an absolute value equation, you need to follow the format |expression| = value. For example, |x - 5| = 3 represents the distance between x and 5 on the number line.

Q: What is the difference between an absolute value equation and a linear equation?

A: An absolute value equation is an equation that involves the absolute value of a quantity, while a linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I solve an absolute value equation?

A: To solve an absolute value equation, you need to consider two cases: one where the expression inside the absolute value is positive, and one where the expression inside the absolute value is negative.

Q: What are some common mistakes to avoid when solving absolute value equations?

A: Some common mistakes to avoid when solving absolute value equations include:

  • Not considering both cases (positive and negative) when solving the equation.
  • Not checking the solutions to make sure they satisfy the original equation.
  • Not using the correct notation (e.g. |x - 5| = 3 instead of x - 5 = 3).

Q: Can absolute value equations be used to represent real-world situations?

A: Yes, absolute value equations can be used to represent real-world situations. For example, the equation |x - 10| = 2 can be used to represent the distance between x and 10 on the number line.

Q: How do I graph an absolute value equation?

A: To graph an absolute value equation, you need to graph the two cases (positive and negative) separately and then combine them.

Q: What are some common applications of absolute value equations?

A: Some common applications of absolute value equations include:

  • Modeling real-world situations, such as distance and time problems.
  • Solving problems involving absolute value, such as finding the distance between two points.
  • Graphing functions, such as absolute value functions.

Q: Can absolute value equations be used to solve systems of equations?

A: Yes, absolute value equations can be used to solve systems of equations. For example, the system of equations |x - 2| = 1 and |y - 3| = 2 can be solved using absolute value equations.

Conclusion

In conclusion, absolute value equations are a powerful tool for representing real-world situations and solving problems. By understanding how to use absolute value equations, we can solve a wide range of problems and represent complex situations in a simple and elegant way.

Additional Resources

For more information on absolute value equations, check out the following resources:

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

Practice Problems

Try solving the following absolute value equations:

  • |x - 5| = 2
  • |x + 3| = 1
  • |x - 10| = 4

Answer Key

  • |x - 5| = 2: x = 7 or x = 3
  • |x + 3| = 1: x = -2 or x = 4
  • |x - 10| = 4: x = 14 or x = 6