Which Number Line Represents The Solutions To ∣ − 2 X ∣ = 4 |-2x| = 4 ∣ − 2 X ∣ = 4 ?

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Introduction

When dealing with absolute value equations, it's essential to understand the concept of distance and how it relates to the number line. The absolute value of a number represents its distance from zero on the number line. In this article, we will explore the solutions to the equation $|-2x| = 4$ and determine which number line represents these solutions.

Understanding Absolute Value Equations

Absolute value equations involve the absolute value of a variable or expression, which is denoted by the symbol $| |$. The absolute value of a number is its distance from zero on the number line. For example, the absolute value of $-3$ is $3$, because $-3$ is $3$ units away from zero on the number line.

When solving absolute value equations, we need to consider two cases: one where the expression inside the absolute value is positive, and one where it is negative. This is because the absolute value of a negative number is positive, and the absolute value of a positive number is also positive.

Solving the Equation $|-2x| = 4$

To solve the equation $|-2x| = 4$, we need to consider two cases:

Case 1: $-2x = 4$

In this case, we can solve for $x$ by dividing both sides of the equation by $-2$:

$$\frac{-2x}{-2} = \frac{4}{-2}$$

$$x = -2$$

So, one solution to the equation $|-2x| = 4$ is $x = -2$.

Case 2: $-2x = -4$

In this case, we can solve for $x$ by dividing both sides of the equation by $-2$:

$$\frac{-2x}{-2} = \frac{-4}{-2}$$

$$x = 2$$

So, another solution to the equation $|-2x| = 4$ is $x = 2$.

Graphing the Solutions on the Number Line

Now that we have found the solutions to the equation $|-2x| = 4$, we can graph them on the number line.

The number line is a horizontal line that represents all possible real numbers. We can mark the solutions $x = -2$ and $x = 2$ on the number line by placing a point at each of these values.

The number line that represents the solutions to $|-2x| = 4$ is a horizontal line that passes through the points $-2$ and $2$.

Conclusion

In this article, we have explored the solutions to the equation $|-2x| = 4$ and determined which number line represents these solutions. We have seen that the equation has two solutions, $x = -2$ and $x = 2$, and that the number line that represents these solutions is a horizontal line that passes through the points $-2$ and $2$.

Frequently Asked Questions

• What is the absolute value of a number? The absolute value of a number is its distance from zero on the number line.
• How do you solve an absolute value equation? 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 it is negative.
• What is the number line that represents the solutions to $|-2x| = 4$? The number line that represents the solutions to $|-2x| = 4$ is a horizontal line that passes through the points $-2$ and $2$.

Further Reading

• Absolute Value Equations: A Comprehensive Guide
• Number Lines: A Visual Representation of Real Numbers
• Solving Equations with Absolute Value: Tips and Tricks
  

Introduction

Absolute value equations can be a challenging topic for many students, but with the right guidance, they can become a breeze. In this article, we will answer some of the most frequently asked questions about absolute value equations, providing you with a comprehensive guide to help you master this topic.

Q&A

Q: What is the absolute value of a number?

A: The absolute value of a number is its distance from zero on the number line. For example, the absolute value of -3 is 3, because -3 is 3 units away from zero on the number line.

Q: How do you 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 it is negative. This is because the absolute value of a negative number is positive, and the absolute value of a positive number is also positive.

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

A: The main difference between an absolute value equation and a regular equation is that absolute value equations involve the absolute value of a variable or expression, which is denoted by the symbol | |. Regular equations do not involve absolute values.

Q: How do you graph absolute value equations on a number line?

A: To graph an absolute value equation on a number line, you need to find the solutions to the equation and mark them on the number line. The number line will have a horizontal line that passes through the points that represent the solutions.

Q: What is the number line that represents the solutions to |-2x| = 4?

A: The number line that represents the solutions to |-2x| = 4 is a horizontal line that passes through the points -2 and 2.

Q: How do you solve absolute value equations with variables on both sides?

A: To solve absolute value equations with variables on both sides, you need to isolate the variable on one side of the equation and then consider the two cases: one where the expression inside the absolute value is positive, and one where it is negative.

Q: What is the absolute value of a fraction?

A: The absolute value of a fraction is the absolute value of the numerator divided by the absolute value of the denominator. For example, the absolute value of -3/4 is 3/4.

Q: How do you solve absolute value equations with decimals?

A: To solve absolute value equations with decimals, you need to follow the same steps as solving absolute value equations with integers. You need to consider the two cases: one where the expression inside the absolute value is positive, and one where it is negative.

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

A: The absolute value of a negative number is the positive value of the number. For example, the absolute value of -3 is 3.

Q: How do you graph absolute value equations with decimals on a number line?

A: To graph absolute value equations with decimals on a number line, you need to find the solutions to the equation and mark them on the number line. The number line will have a horizontal line that passes through the points that represent the solutions.

Conclusion

In this article, we have answered some of the most frequently asked questions about absolute value equations, providing you with a comprehensive guide to help you master this topic. We have covered topics such as the definition of absolute value, solving absolute value equations, graphing absolute value equations on a number line, and more.

Frequently Asked Questions

• What is the absolute value of a number?
• How do you solve an absolute value equation?
• What is the difference between an absolute value equation and a regular equation?
• How do you graph absolute value equations on a number line?
• What is the number line that represents the solutions to |-2x| = 4?
• How do you solve absolute value equations with variables on both sides?
• What is the absolute value of a fraction?
• How do you solve absolute value equations with decimals?
• What is the absolute value of a negative number?
• How do you graph absolute value equations with decimals on a number line?

Further Reading

• Absolute Value Equations: A Comprehensive Guide
• Number Lines: A Visual Representation of Real Numbers
• Solving Equations with Absolute Value: Tips and Tricks