Solve For $x$:$7x - 10 = 2x - 30$ \$x =$[/tex\] $\square$

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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 specific type of linear equation, which is the equation of the form $ax = b$. We will use the equation $7x - 10 = 2x - 30$ as an example to demonstrate the step-by-step process of solving linear equations.

What are Linear Equations?

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A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. Linear equations 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, graphing, and substitution.

The Equation $7x - 10 = 2x - 30$

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The equation $7x - 10 = 2x - 30$ is a linear equation in which the highest power of the variable $x$ is 1. To solve this equation, we need to isolate the variable $x$ on one side of the equation.

Step 1: Add 10 to Both Sides of the Equation

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The first step in solving the equation $7x - 10 = 2x - 30$ is to add 10 to both sides of the equation. This will eliminate the negative term on the left-hand side of the equation.

# Define the equation
equation = "7x - 10 = 2x - 30"

# Add 10 to both sides of the equation
new_equation = equation.replace("- 10", "+ 10")
print(new_equation)

Step 2: Simplify the Equation

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After adding 10 to both sides of the equation, we get $7x = 2x - 20$. The next step is to simplify the equation by combining like terms.

# Simplify the equation
simplified_equation = "7x = 2x - 20"
print(simplified_equation)

Step 3: Subtract 2x from Both Sides of the Equation

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The next step is to subtract 2x from both sides of the equation. This will eliminate the variable $x$ on the right-hand side of the equation.

# Subtract 2x from both sides of the equation
new_equation = simplified_equation.replace("2x", "")
print(new_equation)

Step 4: Simplify the Equation

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After subtracting 2x from both sides of the equation, we get $5x = -20$. The next step is to simplify the equation by dividing both sides of the equation by 5.

# Simplify the equation
simplified_equation = "5x = -20"
print(simplified_equation)

Step 5: Divide Both Sides of the Equation by 5

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The final step is to divide both sides of the equation by 5. This will give us the value of the variable $x$.

# Divide both sides of the equation by 5
final_equation = simplified_equation.replace("5x", "")
print(final_equation)

Conclusion

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In this article, we have demonstrated the step-by-step process of solving a linear equation. We have used the equation $7x - 10 = 2x - 30$ as an example to illustrate the process. By following these steps, we can solve linear equations and find the value of the variable $x$.

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.

Q: How do I solve a linear equation?

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

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 (in this case, $x$) is 1. A quadratic equation is an equation in which the highest power of the variable (in this case, $x$) is 2.

References

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• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f8f7d
• [2] Math Open Reference. (n.d.). Linear Equations. Retrieved from https://www.mathopenref.com/linearequations.html

Additional Resources

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• [1] Khan Academy. (n.d.). Algebra. Retrieved from https://www.khanacademy.org/math/algebra
• [2] Math Open Reference. (n.d.). Algebra. Retrieved from https://www.mathopenref.com/algebra.html

Final Answer

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The final answer is $\boxed{x = -4}$.

=====================================================

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 provide a Q&A guide to help students understand and solve linear equations.

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. Linear equations 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 $x$ on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides of the equation by the same value.

Q: What is the difference between a linear equation and a quadratic 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. A quadratic equation is an equation in which the highest power of the variable (in this case, $x$) is 2.

Q: How do I simplify a linear equation?

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A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, in the equation $2x + 3x = 5x$, the like terms are $2x$ and $3x$.

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

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A: To isolate the variable $x$ in a linear equation, you need to get rid of any constants that are being added or subtracted from the variable. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the order of operations in solving linear equations?

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A: The order of operations in solving linear equations is:

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 check my answer in a linear equation?

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A: To check your answer in a linear equation, you need to plug your solution back into the original equation and see if it is true. If it is true, then your solution is correct.

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

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

• Not following the order of operations
• Not combining like terms
• Not isolating the variable $x$ correctly
• Not checking your answer

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

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A: To solve a linear equation with fractions, you need to get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

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

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A: To solve a linear equation with decimals, you need to get rid of the decimals by multiplying both sides of the equation by a power of 10.

Q: What are some real-world applications of linear equations?

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A: Some real-world applications of linear equations include:

• Modeling population growth
• Calculating interest rates
• Determining the cost of goods
• Solving problems in physics and engineering

Conclusion

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In this article, we have provided a Q&A guide to help students understand and solve linear equations. We have covered topics such as the definition of a linear equation, how to solve a linear equation, and common mistakes to avoid. We have also discussed real-world applications of linear equations and provided tips for solving linear equations with fractions and decimals.

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.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable $x$ on one side of the equation.

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 (in this case, $x$) is 1. A quadratic equation is an equation in which the highest power of the variable (in this case, $x$) is 2.

References

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• [1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f8f7d
• [2] Math Open Reference. (n.d.). Linear Equations. Retrieved from https://www.mathopenref.com/linearequations.html

Additional Resources

---

• [1] Khan Academy. (n.d.). Algebra. Retrieved from https://www.khanacademy.org/math/algebra
• [2] Math Open Reference. (n.d.). Algebra. Retrieved from https://www.mathopenref.com/algebra.html

Final Answer

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The final answer is $\boxed{x = -4}$.