Solve For { X $} . . . { 7x + 3 = 31 \}

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Introduction

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving a linear equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. We will use the given equation $7x + 3 = 31$ as an example to demonstrate the step-by-step process of solving for $x$.

Understanding the Equation

The given equation is $7x + 3 = 31$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The equation consists of two terms: $7x$ and $3$. The constant term $3$ is added to the product of $7$ and $x$. Our goal is to get rid of the constant term and isolate the variable $x$.

Step 1: Subtract 3 from Both Sides

To isolate the variable $x$, we need to get rid of the constant term $3$. We can do this by subtracting $3$ from both sides of the equation. This will keep the equation balanced and ensure that the variable $x$ remains on one side of the equation.

$$7x + 3 - 3 = 31 - 3$$

Simplifying the equation, we get:

$$7x = 28$$

Step 2: Divide Both Sides by 7

Now that we have isolated the variable $x$ on one side of the equation, we need to get rid of the coefficient $7$. We can do this by dividing both sides of the equation by $7$. This will give us the value of $x$.

$$\frac{7x}{7} = \frac{28}{7}$$

Simplifying the equation, we get:

$$x = 4$$

Conclusion

In this article, we solved the linear equation $7x + 3 = 31$ by isolating the variable $x$ on one side of the equation. We used the steps of subtracting $3$ from both sides and dividing both sides by $7$ to get the value of $x$. The final answer is $x = 4$.

Tips and Tricks

• When solving linear equations, it's essential to keep the equation balanced by performing the same operation on both sides.
• Use the order of operations (PEMDAS) to simplify the equation and isolate the variable.
• Check your work by plugging the solution back into the original equation to ensure that it's true.

Real-World Applications

Solving linear equations has numerous real-world applications in various fields, including:

• Physics: Solving linear equations is essential in physics to describe the motion of objects and calculate their velocities and accelerations.
• Engineering: Linear equations are used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Solving linear equations is used in economics to model and analyze economic systems, including supply and demand curves.

Common Mistakes

• Failing to keep the equation balanced by performing the same operation on both sides.
• Not using the order of operations (PEMDAS) to simplify the equation and isolate the variable.
• Not checking the work by plugging the solution back into the original equation to ensure that it's true.

Additional Resources

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

Final Thoughts

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a given equation. By following the steps outlined in this article, you can solve linear equations with ease and apply the concepts to real-world problems. Remember to keep the equation balanced, use the order of operations, and check your work to ensure that the solution is true.

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Introduction

In our previous article, we solved the linear equation $7x + 3 = 31$ by isolating the variable $x$ on one side of the equation. We used the steps of subtracting $3$ from both sides and dividing both sides by $7$ to get the value of $x$. In this article, we will answer some frequently asked questions (FAQs) related to solving linear equations.

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's 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 on one side of the equation. You can do this by performing the same operation on both sides of the equation, such as adding or subtracting the same value, or multiplying or dividing both sides by the same value.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. PEMDAS stands for:

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

Q: How do I check my work when solving a linear equation?

A: To check your work, plug the solution back into the original equation and see if it's true. If the solution satisfies the original equation, then you've solved the equation correctly.

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

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

• Failing to keep the equation balanced by performing the same operation on both sides.
• Not using the order of operations (PEMDAS) to simplify the equation and isolate the variable.
• Not checking the work by plugging the solution back into the original equation to ensure that it's true.

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

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 check your work to ensure that the solution is true.

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

A: Linear equations have numerous real-world applications in various fields, including physics, engineering, and economics. To apply linear equations to real-world problems, you need to understand the concepts and techniques involved in solving linear equations and to use them to model and analyze real-world systems.

Q: What are some additional resources for learning about linear equations?

A: Some additional resources for learning about linear equations include:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations
• Online tutorials and videos
• Textbooks and workbooks

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a given equation. By following the steps outlined in this article and using the resources provided, you can solve linear equations with ease and apply the concepts to real-world problems.

Tips and Tricks

• Practice solving linear equations regularly to build your skills and confidence.
• Use online resources and tutorials to supplement your learning.
• Check your work by plugging the solution back into the original equation to ensure that it's true.
• Apply linear equations to real-world problems to see the relevance and importance of the concept.

Final Thoughts

Solving linear equations is a critical skill that has numerous real-world applications. By understanding the concepts and techniques involved in solving linear equations, you can apply them to a wide range of problems and situations. Remember to practice regularly, use online resources, and check your work to ensure that the solution is true.