Select The Correct Answer.Samantha Made A Device That Pours 300 Ml Of Hot Wax Into Molds. Due To A Hardware Flaw, The Device Pours 4 Ml Less Than Or More Than 300 Ml Of Wax Into The Molds. The Following Absolute Value Equation Can Be Used To Determine

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Introduction

In mathematics, absolute value equations are used to represent real-world problems that involve distances, temperatures, and other quantities that can be positive or negative. In this article, we will explore how to solve absolute value equations using a real-world example. We will use the scenario of a device that pours hot wax into molds to demonstrate how to apply absolute value equations to solve problems.

The Problem

Samantha made a device that pours 300 ml of hot wax into molds. However, due to a hardware flaw, the device pours 4 ml less than or more than 300 ml of wax into the molds. We need to determine the amount of wax that the device actually pours into the molds.

Setting Up the Equation

Let's represent the amount of wax that the device pours into the molds as x. Since the device pours 4 ml less than or more than 300 ml of wax, we can set up the following absolute value equation:

|x - 300| = 4

Understanding Absolute Value Equations

Absolute value equations are equations that involve the absolute value of a quantity. The absolute value of a quantity is its distance from zero, without considering direction. In this case, the absolute value of x - 300 represents the distance between x and 300.

Solving the Equation

To solve the equation |x - 300| = 4, we need to consider two cases:

Case 1: x - 300 = 4

In this case, we can add 300 to both sides of the equation to solve for x:

x - 300 + 300 = 4 + 300 x = 304

Case 2: x - 300 = -4

In this case, we can add 300 to both sides of the equation to solve for x:

x - 300 + 300 = -4 + 300 x = 296

Conclusion

In this article, we used a real-world example to demonstrate how to solve absolute value equations. We set up an equation to represent the amount of wax that a device pours into molds, and then solved the equation using two cases. The solutions to the equation were x = 304 and x = 296, which represent the amount of wax that the device pours into the molds.

Real-World Applications

Absolute value equations have many real-world applications, including:

  • Distance and speed: Absolute value equations can be used to represent the distance between two objects or the speed of an object.
  • Temperature: Absolute value equations can be used to represent the temperature of an object or the difference between two temperatures.
  • Finance: Absolute value equations can be used to represent the difference between two financial values or the amount of money that is owed.

Tips and Tricks

When solving absolute value equations, remember to consider two cases:

  • Case 1: The quantity inside the absolute value is positive.
  • Case 2: The quantity inside the absolute value is negative.

By considering these two cases, you can solve absolute value equations and apply them to real-world problems.

Practice Problems

Try solving the following absolute value equations:

  • |x - 200| = 3
  • |x + 100| = 2
  • |x - 50| = 1

Conclusion

Q&A: Solving Absolute Value Equations

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, without considering direction.

Q: How do I set up an absolute value equation?

A: To set up an absolute value equation, you need to represent the quantity that you are interested in as x. Then, you need to write an equation that involves the absolute value of x. For example, if you are interested in the distance between x and 300, you can write the equation |x - 300| = 4.

Q: How do I solve an absolute value equation?

A: To solve an absolute value equation, you need to consider two cases:

  • Case 1: The quantity inside the absolute value is positive.
  • Case 2: The quantity inside the absolute value is negative.

You need to solve the equation for each case and then combine the solutions.

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: Make sure to consider both Case 1 and Case 2 when solving an absolute value equation.
  • Not checking the solutions: Make sure to check the solutions to see if they are valid.
  • Not using the correct notation: Make sure to use the correct notation when writing absolute value equations.

Q: How do I apply absolute value equations to real-world problems?

A: Absolute value equations can be applied to a wide range of real-world problems, including:

  • Distance and speed: Absolute value equations can be used to represent the distance between two objects or the speed of an object.
  • Temperature: Absolute value equations can be used to represent the temperature of an object or the difference between two temperatures.
  • Finance: Absolute value equations can be used to represent the difference between two financial values or the amount of money that is owed.

Q: What are some tips and tricks for solving absolute value equations?

A: Some tips and tricks for solving absolute value equations include:

  • Use a number line: A number line can be a helpful tool when solving absolute value equations.
  • Check the solutions: Make sure to check the solutions to see if they are valid.
  • Use the correct notation: Make sure to use the correct notation when writing absolute value equations.

Q: How do I practice solving absolute value equations?

A: There are many ways to practice solving absolute value equations, including:

  • Working on practice problems: Try solving practice problems to get a feel for how to solve absolute value equations.
  • Using online resources: There are many online resources available that can help you practice solving absolute value equations.
  • Asking a teacher or tutor for help: If you are having trouble solving absolute value equations, don't be afraid to ask a teacher or tutor for help.

Conclusion

In this article, we have covered the basics of solving absolute value equations. We have discussed how to set up an absolute value equation, how to solve it, and how to apply it to real-world problems. We have also provided some tips and tricks for solving absolute value equations and some practice problems to help you get started. By following these steps and practicing regularly, you can become proficient in solving absolute value equations and apply them to a wide range of real-world problems.