Solve The Equation: 1. $1.2x = 6$ Check Your Solution.

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Introduction

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Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, $1.2x = 6$, and provide a step-by-step guide on how to check the solution.

What is a Linear Equation?

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A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation and graphical representation.

Solving the Equation: $1.2x = 6$

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To solve the equation $1.2x = 6$, we need to isolate the variable $x$. We can do this by dividing both sides of the equation by 1.2.

Step 1: Divide Both Sides by 1.2

To isolate $x$, we need to get rid of the coefficient 1.2. We can do this by dividing both sides of the equation by 1.2.

# Import necessary modules
import math

# Define variables
a = 1.2
b = 6

# Divide both sides by 1.2
x = b / a

Step 2: Simplify the Expression

After dividing both sides by 1.2, we get $x = 6/1.2$. We can simplify this expression by dividing 6 by 1.2.

# Simplify the expression
x = 6 / 1.2

Step 3: Calculate the Value of $x$

Now that we have simplified the expression, we can calculate the value of $x$.

# Calculate the value of x
x = 5.0

Checking the Solution

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To check the solution, we need to plug the value of $x$ back into the original equation and verify that it is true.

Step 1: Plug the Value of $x$ Back into the Equation

We will plug the value of $x$ back into the original equation $1.2x = 6$.

# Plug the value of x back into the equation
a = 1.2
b = 6
x = 5.0

# Check if the equation is true
if a * x == b:
    print("The solution is correct.")
else:
    print("The solution is incorrect.")

Step 2: Verify the Equation

We will verify that the equation is true by checking if the left-hand side of the equation is equal to the right-hand side.

# Verify the equation
a = 1.2
b = 6
x = 5.0

# Check if the equation is true
if a * x == b:
    print("The equation is true.")
else:
    print("The equation is false.")

Conclusion

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In this article, we solved the linear equation $1.2x = 6$ using algebraic manipulation and provided a step-by-step guide on how to check the solution. We also used Python code to demonstrate the steps involved in solving the equation and checking the solution. By following these steps, students can master the skill of solving linear equations and apply it to a wide range of mathematical problems.

Frequently Asked Questions

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Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable $x$. You can do this by dividing both sides of the equation by the coefficient of $x$.

Q: How do I check the solution?

A: To check the solution, you need to plug the value of $x$ back into the original equation and verify that it is true.

Additional Resources

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For more information on solving linear equations, you can refer to the following resources:

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

References

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• [1] Khan Academy. (n.d.). Solving Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4f/solving-linear-equations
• [2] Mathway. (n.d.). Solving Linear Equations. Retrieved from https://www.mathway.com/subjects/Algebra/Solving-Linear-Equations
• [3] Wolfram Alpha. (n.d.). Solving Linear Equations. Retrieved from https://www.wolframalpha.com/input/?i=solving+linear+equations
  

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Introduction

---

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to solve them correctly. In this article, we will provide a Q&A guide on solving linear equations, covering various topics and scenarios.

Q: What is a linear equation?

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A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

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A: To solve a linear equation, you need to isolate the variable $x$. You can do this by dividing both sides of the equation by the coefficient of $x$.

Q: What is the coefficient of $x$?

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A: The coefficient of $x$ is the number that is multiplied by $x$ in the equation. For example, in the equation $2x = 6$, the coefficient of $x$ is 2.

Q: How do I check the solution?

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A: To check the solution, you need to plug the value of $x$ back into the original equation and verify that it is true.

Q: What if the equation has a fraction?

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A: If the equation has a fraction, you can multiply both sides of the equation by the denominator to eliminate the fraction.

Q: What if the equation has a negative sign?

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A: If the equation has a negative sign, you can multiply both sides of the equation by -1 to eliminate the negative sign.

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

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A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the steps involved in solving the equation and to verify the solution.

Q: How do I solve a linear equation with multiple variables?

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A: To solve a linear equation with multiple variables, you need to isolate one variable at a time. You can use substitution or elimination methods to solve the equation.

Q: What if the equation has a variable on both sides?

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A: If the equation has a variable on both sides, you can add or subtract the same value to both sides of the equation to eliminate the variable.

Q: Can I use algebraic manipulation to solve linear equations?

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A: Yes, you can use algebraic manipulation to solve linear equations. This involves using various techniques such as addition, subtraction, multiplication, and division to isolate the variable.

Q: How do I verify the solution?

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A: To verify the solution, you need to plug the value of $x$ back into the original equation and check if it is true.

Q: What if I get a different solution?

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A: If you get a different solution, it's possible that the equation has multiple solutions or that there is an error in the solution.

Q: Can I use technology to solve linear equations?

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A: Yes, you can use technology such as calculators or computer software to solve linear equations. However, it's essential to understand the steps involved in solving the equation and to verify the solution.

Q: How do I graph a linear equation?

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A: To graph a linear equation, you need to plot the points on a coordinate plane and draw a line through the points.

Q: What is the slope of a linear equation?

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A: The slope of a linear equation is the ratio of the change in $y$ to the change in $x$.

Q: How do I find the slope of a linear equation?

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A: To find the slope of a linear equation, you need to use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Q: What is the y-intercept of a linear equation?

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A: The y-intercept of a linear equation is the point where the line intersects the y-axis.

Q: How do I find the y-intercept of a linear equation?

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A: To find the y-intercept of a linear equation, you need to use the formula $b = y_1 - mx_1$.

Q: Can I use linear equations to model real-world problems?

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A: Yes, you can use linear equations to model real-world problems such as cost, revenue, and profit.

Q: How do I use linear equations to model real-world problems?

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A: To use linear equations to model real-world problems, you need to identify the variables and the relationships between them.

Q: What are some common applications of linear equations?

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A: Some common applications of linear equations include finance, science, engineering, and economics.

Q: How do I apply linear equations to finance?

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A: To apply linear equations to finance, you need to use linear equations to model cost, revenue, and profit.

Q: How do I apply linear equations to science?

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A: To apply linear equations to science, you need to use linear equations to model physical phenomena such as motion and gravity.

Q: How do I apply linear equations to engineering?

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A: To apply linear equations to engineering, you need to use linear equations to model physical systems such as bridges and buildings.

Q: How do I apply linear equations to economics?

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A: To apply linear equations to economics, you need to use linear equations to model economic systems such as supply and demand.

Conclusion

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In this article, we have provided a Q&A guide on solving linear equations, covering various topics and scenarios. We hope that this guide has been helpful in understanding how to solve linear equations and how to apply them to real-world problems.

Frequently Asked Questions

---

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It can be written in the form $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable $x$. You can do this by dividing both sides of the equation by the coefficient of $x$.

Q: What if the equation has a fraction?

A: If the equation has a fraction, you can multiply both sides of the equation by the denominator to eliminate the fraction.

Q: What if the equation has a negative sign?

A: If the equation has a negative sign, you can multiply both sides of the equation by -1 to eliminate the negative sign.

Additional Resources

---

For more information on solving linear equations, you can refer to the following resources:

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

References

---

• [1] Khan Academy. (n.d.). Solving Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4f/solving-linear-equations
• [2] Mathway. (n.d.). Solving Linear Equations. Retrieved from https://www.mathway.com/subjects/Algebra/Solving-Linear-Equations
• [3] Wolfram Alpha. (n.d.). Solving Linear Equations. Retrieved from https://www.wolframalpha.com/input/?i=solving+linear+equations