Select The Correct Answer.What Is The Solution To The Equation ∣ 5 − X ∣ = 13 |5-x|=13 ∣5 − X ∣ = 13 ?A. X = 8 X=8 X = 8 B. X = − 8 X=-8 X = − 8 Or X = 18 X=18 X = 18 C. X = − 18 X=-18 X = − 18 D. X = − 18 X=-18 X = − 18 Or X = 8 X=8 X = 8

Introduction

Absolute value equations are a fundamental concept in mathematics, and solving them requires a clear understanding of the properties of absolute value. In this article, we will explore the solution to the equation $|5-x|=13$ and provide a step-by-step guide on how to solve it.

Understanding Absolute Value

Absolute value, denoted by the symbol $| |$, is a mathematical operation that returns the distance of a number from zero on the number line. For example, the absolute value of $-3$ is $3$, and the absolute value of $4$ is also $4$. The absolute value of a number is always non-negative.

The Equation $|5-x|=13$

The equation $|5-x|=13$ can be read as "the absolute value of $5-x$ is equal to $13$". To solve this equation, we need to find the values of $x$ that satisfy this condition.

Step 1: Isolate the Absolute Value Expression

The first step in solving the equation is to isolate the absolute value expression. In this case, the absolute value expression is $5-x$. To isolate it, we can subtract $5$ from both sides of the equation:

$$|5-x|=13$$

$$-(5-x)=13$$

$$-5+x=13$$

$$x-5=13$$

Step 2: Write Two Separate Equations

When we have an absolute value equation, we can write two separate equations by removing the absolute value sign and changing the sign of the expression inside the absolute value. In this case, we have:

$$x-5=13$$

$$x-5=-13$$

Step 3: Solve Each Equation

Now that we have two separate equations, we can solve each one individually.

Equation 1: $x-5=13$

To solve this equation, we can add $5$ to both sides:

$$x-5+5=13+5$$

$$x=18$$

Equation 2: $x-5=-13$

To solve this equation, we can add $5$ to both sides:

$$x-5+5=-13+5$$

$$x=-8$$

Conclusion

In conclusion, the solution to the equation $|5-x|=13$ is $x=-8$ or $x=18$. These two values satisfy the equation and are the correct answers.

Comparison with the Options

Now that we have solved the equation, let's compare our solution with the options provided:

A. $x=8$ B. $x=-8$ or $x=18$ C. $x=-18$ D. $x=-18$ or $x=8$

Our solution matches option B, which is $x=-8$ or $x=18$.

Final Answer

The final answer is:

• B. $x=-8$ or $x=18$

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Introduction

In our previous article, we explored the solution to the equation $|5-x|=13$ and provided a step-by-step guide on how to solve it. In this article, we will answer some frequently asked questions about solving absolute value equations.

Q&A

Q: What is the definition of absolute value?

A: Absolute value, denoted by the symbol $| |$, is a mathematical operation that returns the distance of a number from zero on the number line. For example, the absolute value of $-3$ is $3$, and the absolute value of $4$ is also $4$.

Q: How do I solve an absolute value equation?

A: To solve an absolute value equation, you need to follow these steps:

1. Isolate the absolute value expression.
2. Write two separate equations by removing the absolute value sign and changing the sign of the expression inside the absolute value.
3. Solve each equation individually.

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

A: An absolute value equation is an equation that contains an absolute value expression, while a linear equation is an equation that contains a linear expression. For example, the equation $|x|=3$ is an absolute value equation, while the equation $x+2=5$ is a linear equation.

Q: Can I use the same method to solve all absolute value equations?

A: No, you cannot use the same method to solve all absolute value equations. The method we used in our previous article is for equations of the form $|a-b|=c$, where $a$, $b$, and $c$ are constants. If you have an equation of the form $|a-b|=c$, where $a$, $b$, and $c$ are variables, you will need to use a different method.

Q: How do I know which values to use when solving an absolute value equation?

A: When solving an absolute value equation, you need to use the values that satisfy the equation. In our previous article, we used the values $x=-8$ and $x=18$ to solve the equation $|5-x|=13$. These values satisfy the equation and are the correct answers.

Q: Can I use absolute value equations to solve real-world problems?

A: Yes, you can use absolute value equations to solve real-world problems. For example, you can use absolute value equations to model the distance between two points on a number line, or to model the amount of money you have in your bank account.

Examples of Absolute Value Equations in Real-World Problems

Example 1: Distance Between Two Points

Suppose you are standing at a point on a number line that is 5 units away from a certain point. If you move 13 units to the left, how far are you from the original point?

To solve this problem, you can use the absolute value equation $|5-x|=13$, where $x$ is the distance between the two points.

Example 2: Bank Account Balance

Suppose you have a bank account with a balance of $100. If you deposit $50, how much money do you have in your account?

To solve this problem, you can use the absolute value equation $|100+x|=50$, where $x$ is the amount of money you deposit.

Conclusion

In conclusion, solving absolute value equations is a useful skill that can be applied to a wide range of real-world problems. By following the steps outlined in this article, you can solve absolute value equations and apply them to solve real-world problems.

Final Tips

• Always read the problem carefully and understand what is being asked.
• Use the correct method to solve the equation.
• Check your work to make sure you have the correct answer.

By following these tips, you can become proficient in solving absolute value equations and apply them to solve real-world problems.