Consider The Equation X 5 − 2 = 11 \frac{x}{5} - 2 = 11 5 X ​ − 2 = 11 .Each Of These Values Might Be The Solution To This Equation. Verify The Correct Solution By Substituting Each Value Into The Equation. Which Is The Correct Solution?A. X = 1.8 X = 1.8 X = 1.8 B. $x =

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore how to solve a linear equation using a step-by-step approach. We will use the equation $\frac{x}{5} - 2 = 11$ as an example and verify the correct solution by substituting each value into the equation.

Understanding the Equation

The given equation is $\frac{x}{5} - 2 = 11$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The equation consists of a fraction, a constant term, and an equal sign. Our goal is to get rid of the fraction and the constant term to find the value of $x$.

Step 1: Add 2 to Both Sides

To get rid of the constant term $-2$, we need to add $2$ to both sides of the equation. This will keep the equation balanced and allow us to simplify it.

$\frac{x}{5} - 2 + 2 = 11 + 2$

Simplifying the equation, we get:

$\frac{x}{5} = 13$

Step 2: Multiply Both Sides by 5

To get rid of the fraction, we need to multiply both sides of the equation by $5$. This will allow us to isolate the variable $x$.

$\frac{x}{5} \times 5 = 13 \times 5$

Simplifying the equation, we get:

$x = 65$

Verifying the Solution

Now that we have found the solution $x = 65$, we need to verify it by substituting it back into the original equation. If the equation holds true, then we have found the correct solution.

Substituting $x = 65$ into the original equation, we get:

$\frac{65}{5} - 2 = 11$

Simplifying the equation, we get:

$13 - 2 = 11$

$11 = 11$

The equation holds true, so we have found the correct solution.

Conclusion

In this article, we have solved the linear equation $\frac{x}{5} - 2 = 11$ using a step-by-step approach. We added $2$ to both sides of the equation to get rid of the constant term, and then multiplied both sides by $5$ to get rid of the fraction. We verified the solution by substituting it back into the original equation, and found that $x = 65$ is the correct solution.

Discussion

Now that we have found the correct solution, let's discuss the other options given in the problem.

A. $x = 1.8$

To verify this solution, we need to substitute it back into the original equation.

$\frac{1.8}{5} - 2 = 11$

Simplifying the equation, we get:

$0.36 - 2 = 11$

$-1.64 \neq 11$

The equation does not hold true, so $x = 1.8$ is not the correct solution.

B. $x = 65$

We have already verified this solution in the previous section, and found that it is the correct solution.

Final Answer

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Introduction

In our previous article, we explored how to solve a linear equation using a step-by-step approach. We used the equation $\frac{x}{5} - 2 = 11$ as an example and verified the correct solution by substituting each value into the equation. In this article, we will answer some frequently asked questions about solving linear equations.

Q&A

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it 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 a linear equation?

A: To solve a linear equation, you need to isolate the variable(s) on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations when solving a linear equation?

A: When solving a linear equation, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I handle fractions in a linear equation?

A: When a linear equation contains a fraction, you can get rid of the fraction by multiplying both sides of the equation by the denominator of the fraction.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

Q: Can I use a calculator to solve a linear equation?

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to verify the solution by substituting it back into the original equation.

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

A: Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations
• Not isolating the variable(s) on one side of the equation
• Not verifying the solution by substituting it back into the original equation

Conclusion

Solving linear equations is an essential skill for students to master. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving linear equations. Remember to always verify your solution by substituting it back into the original equation.

Additional Resources

For more information on solving linear equations, check out the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Final Answer

The correct solution to the equation $\frac{x}{5} - 2 = 11$ is $x = 65$.