Solve For $x$:$7x - 10 = 2x - 30$Answer: $x = \square$

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Introduction

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Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill to master. In this article, we will focus on solving a specific type of linear equation, which is the equation with one variable. We will use the given equation $7x - 10 = 2x - 30$ as an example to demonstrate the step-by-step process of solving for the variable $x$.

What is a Linear Equation?

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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, and $x$ is the variable. Linear equations can be solved using various methods, including addition, subtraction, multiplication, and division.

The Given Equation

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The given equation is $7x - 10 = 2x - 30$. Our goal is to isolate the variable $x$ and find its value. To do this, we will use the following steps:

Step 1: Add 10 to Both Sides of the Equation

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The first step is to add 10 to both sides of the equation to get rid of the negative term on the left-hand side. This gives us:

$7x - 10 + 10 = 2x - 30 + 10$

Simplifying the equation, we get:

$7x = 2x - 20$

Step 2: 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 to get rid of the variable term on the right-hand side. This gives us:

$7x - 2x = 2x - 2x - 20$

Simplifying the equation, we get:

$5x = -20$

Step 3: 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 to solve for $x$. This gives us:

$\frac{5x}{5} = \frac{-20}{5}$

Simplifying the equation, we get:

$x = -4$

Conclusion

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In this article, we have demonstrated the step-by-step process of solving a linear equation with one variable. We used the given equation $7x - 10 = 2x - 30$ as an example and showed how to isolate the variable $x$ by adding, subtracting, multiplying, and dividing both sides of the equation. The final answer is $x = -4$.

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(s) is 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use the following steps: add, subtract, multiply, and divide both sides of the equation to isolate the variable.

Q: What is the final answer to the given equation?

A: The final answer to the given equation $7x - 10 = 2x - 30$ is $x = -4$.

Tips and Tricks

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Tip 1: Use the Order of Operations

When solving a linear equation, make sure to follow the order of operations (PEMDAS): parentheses, exponents, multiplication and division, and addition and subtraction.

Tip 2: Check Your Work

After solving a linear equation, make sure to check your work by plugging the solution back into the original equation.

Tip 3: Practice, Practice, Practice

The more you practice solving linear equations, the more comfortable you will become with the process.

Real-World Applications

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Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

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In conclusion, solving linear equations is a crucial skill to master in mathematics. By following the step-by-step process outlined in this article, you can solve linear equations with ease. Remember to use the order of operations, check your work, and practice, practice, practice. With these tips and tricks, you will become a master of solving linear equations in no time.

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Introduction

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In our previous article, we discussed the step-by-step process of solving linear equations with one variable. However, we know that practice makes perfect, and there's no better way to practice than by answering questions. In this article, we will provide a Q&A guide to help you reinforce your understanding of solving linear equations.

Q&A Guide

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Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to add, subtract, multiply, or divide both sides of the equation to get rid of any constants on the same side as the variable.

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

A: To isolate the variable in a linear equation, you can use the following steps:

1. Add, subtract, multiply, or divide both sides of the equation to get rid of any constants on the same side as the variable.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original 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(s) is 1, whereas a quadratic equation is an equation in which the highest power of the variable(s) is 2.

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

A: To solve a linear equation with fractions, you can follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original equation.

Q: What is the final answer to the equation $2x + 5 = 11$?

A: To solve the equation $2x + 5 = 11$, we can follow these steps:

1. Subtract 5 from both sides of the equation to get rid of the constant term on the same side as the variable.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original equation.

$2x + 5 - 5 = 11 - 5$

$2x = 6$

$\frac{2x}{2} = \frac{6}{2}$

$x = 3$

Therefore, the final answer to the equation $2x + 5 = 11$ is $x = 3$.

Q: What is the final answer to the equation $x - 2 = 7$?

A: To solve the equation $x - 2 = 7$, we can follow these steps:

1. Add 2 to both sides of the equation to get rid of the constant term on the same side as the variable.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original equation.

$x - 2 + 2 = 7 + 2$

$x = 9$

Therefore, the final answer to the equation $x - 2 = 7$ is $x = 9$.

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

A: To solve a linear equation with decimals, you can follow these steps:

1. Multiply both sides of the equation by 10 to eliminate the decimals.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original equation.

Q: What is the final answer to the equation $0.5x + 2 = 6$?

A: To solve the equation $0.5x + 2 = 6$, we can follow these steps:

1. Multiply both sides of the equation by 10 to eliminate the decimals.
2. Subtract 2 from both sides of the equation to get rid of the constant term on the same side as the variable.
3. Use the order of operations (PEMDAS) to simplify the equation.
4. Check your work by plugging the solution back into the original equation.

$10(0.5x + 2) = 10(6)$

$5x + 20 = 60$

$5x + 20 - 20 = 60 - 20$

$5x = 40$

$\frac{5x}{5} = \frac{40}{5}$

$x = 8$

Therefore, the final answer to the equation $0.5x + 2 = 6$ is $x = 8$.

Conclusion

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In this Q&A guide, we have provided answers to some of the most common questions about solving linear equations. We have covered topics such as isolating the variable, solving linear equations with fractions, decimals, and more. By practicing these questions and following the step-by-step process outlined in this guide, you will become a master of solving linear equations in no time.

Frequently Asked Questions

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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, whereas a quadratic equation is an equation in which the highest power of the variable(s) is 2.

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

A: To solve a linear equation with fractions, you can follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original equation.

Q: What is the final answer to the equation $2x + 5 = 11$?

A: The final answer to the equation $2x + 5 = 11$ is $x = 3$.

Q: What is the final answer to the equation $x - 2 = 7$?

A: The final answer to the equation $x - 2 = 7$ is $x = 9$.

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

A: To solve a linear equation with decimals, you can follow these steps:

1. Multiply both sides of the equation by 10 to eliminate the decimals.
2. Use the order of operations (PEMDAS) to simplify the equation.
3. Check your work by plugging the solution back into the original equation.

Tips and Tricks

---

Tip 1: Use the Order of Operations

When solving a linear equation, make sure to follow the order of operations (PEMDAS): parentheses, exponents, multiplication and division, and addition and subtraction.

Tip 2: Check Your Work

After solving a linear equation, make sure to check your work by plugging the solution back into the original equation.

Tip 3: Practice, Practice, Practice

The more you practice solving linear equations, the more comfortable you will become with the process.

Real-World Applications

---

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

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In conclusion, solving linear equations is a crucial skill to master in mathematics. By following the step-by-step process outlined in this guide and practicing with these questions, you will become a master of solving linear equations in no time. Remember to use the order of operations, check your work, and practice, practice, practice. With these tips and tricks, you will be well on your way to becoming a math whiz.