Solve For X X X .1. ${ \begin{align*} 2x + 38 + X + 20 + 3x &= 360 \ 6x + 58 &= 360 \ x &= 50.33 \end{align*} }$2. Plug In X X X And Subtract The Angles You Have.

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 focus on solving linear equations with one variable, specifically the equation $2x + 38 + x + 20 + 3x = 360$. We will break down the solution step by step and provide a clear explanation of each step.

Step 1: Simplify the Equation

The given equation is $2x + 38 + x + 20 + 3x = 360$. To simplify the equation, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.

# Import necessary modules
import sympy as sp
x = sp.symbols('x')

equation = 2x + 38 + x + 20 + 3x - 360

simplified_equation = sp.simplify(equation)

The simplified equation is $6x + 58 = 360$.

Step 2: Isolate the Variable

To isolate the variable, we need to get rid of the constant term on the left-hand side of the equation. We can do this by subtracting 58 from both sides of the equation.

# Subtract 58 from both sides of the equation
isolated_equation = simplified_equation - 58

The isolated equation is $6x = 302$.

Step 3: Solve for $x$

To solve for $x$, we need to get rid of the coefficient of $x$ on the left-hand side of the equation. We can do this by dividing both sides of the equation by 6.

# Divide both sides of the equation by 6
solution = isolated_equation / 6

The solution is $x = 50.33$.

Discussion

Now that we have solved the equation, let's discuss the steps we took to get there. The first step was to simplify the equation by combining like terms. This helped us to get rid of unnecessary terms and make the equation easier to work with.

The second step was to isolate the variable by subtracting 58 from both sides of the equation. This helped us to get rid of the constant term on the left-hand side of the equation.

The third step was to solve for $x$ by dividing both sides of the equation by 6. This helped us to get rid of the coefficient of $x$ on the left-hand side of the equation.

Conclusion

Solving linear equations is an important skill for students to master. By following the steps outlined in this article, we can solve linear equations with one variable. The key is to simplify the equation, isolate the variable, and solve for $x$.

Example 2: Plug in $x$ and Subtract the Angles

Let's say we have two angles, $A$ and $B$, and we want to find the measure of angle $C$ such that $A + B + C = 360$. We can plug in $x = 50.33$ and subtract the angles to find the measure of angle $C$.

# Define the angles
A = 120
B = 150

C = 360 - A - B

The measure of angle $C$ is $90$.

Conclusion

In this article, we solved a linear equation with one variable and discussed the steps we took to get there. We also provided an example of how to plug in $x$ and subtract the angles to find the measure of angle $C$. By following the steps outlined in this article, students can master the skill of solving linear equations and apply it to real-world problems.

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it has many real-world applications. By mastering the skill of solving linear equations, students can apply it to problems in physics, engineering, and other fields. We hope this article has provided a clear and concise guide to solving linear equations, and we encourage students to practice solving linear equations to become proficient in this skill.

References

• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f-linear-equations/x2f-linear-equations-topic/x2f-linear-equations-topic-article
• [2] Mathway. (n.d.). Linear Equations. Retrieved from https://www.mathway.com/subjects/linear-equations

Glossary

• Linear Equation: An equation in which the highest power of the variable is 1.
• Variable: A letter or symbol that represents a value that can change.
• Coefficient: A number that is multiplied by a variable.
• Constant Term: A term that does not contain a variable.
• Like Terms: Terms that have the same variable raised to the same power.
  Solving Linear Equations: A Q&A Guide =====================================

Introduction

In our previous article, we discussed how to solve linear equations with one variable. In this article, we will provide a Q&A guide to help students understand the concepts and techniques involved in solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, the equation $2x + 3 = 5$ is a linear equation because the highest power of the variable $x$ is 1.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. For example, in the equation $2x + 3x + 4$, the like terms are $2x$ and $3x$. You can combine these terms by adding their coefficients, which gives you $5x + 4$.

Q: How do I isolate the variable in a linear equation?

A: To isolate the variable in a linear equation, you need to get rid of the constant term on the left-hand side of the equation. You can do this by subtracting the constant term from both sides of the equation. For example, in the equation $2x + 3 = 5$, you can subtract 3 from both sides to get $2x = 2$.

Q: How do I solve for the variable in a linear equation?

A: To solve for the variable in a linear equation, you need to get rid of the coefficient of the variable on the left-hand side of the equation. You can do this by dividing both sides of the equation by the coefficient. For example, in the equation $2x = 2$, you can divide both sides by 2 to get $x = 1$.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $2x + 3 = 5$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, in the equation $\frac{2}{3}x + 1 = 2$, you can multiply both sides by 3 to get $2x + 3 = 6$.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by a power of 10. For example, in the equation $2.5x + 3 = 5.2$, you can multiply both sides by 10 to get $25x + 30 = 52$.

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

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

• Not simplifying the equation before solving it
• Not isolating the variable before solving for it
• Not checking the solution to make sure it is correct
• Not using the correct order of operations when solving the equation

Conclusion

Solving linear equations is an important skill for students to master. By following the steps outlined in this article, students can solve linear equations with confidence and accuracy. Remember to simplify the equation, isolate the variable, and solve for the variable to get the correct solution.

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it has many real-world applications. By mastering the skill of solving linear equations, students can apply it to problems in physics, engineering, and other fields. We hope this article has provided a clear and concise guide to solving linear equations, and we encourage students to practice solving linear equations to become proficient in this skill.

References

• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f-linear-equations/x2f-linear-equations-topic/x2f-linear-equations-topic-article
• [2] Mathway. (n.d.). Linear Equations. Retrieved from https://www.mathway.com/subjects/linear-equations

Glossary

• Linear Equation: An equation in which the highest power of the variable is 1.
• Variable: A letter or symbol that represents a value that can change.
• Coefficient: A number that is multiplied by a variable.
• Constant Term: A term that does not contain a variable.
• Like Terms: Terms that have the same variable raised to the same power.
• Least Common Multiple (LCM): The smallest multiple that two or more numbers have in common.
• Order of Operations: A set of rules that dictate the order in which mathematical operations should be performed.