Solve For { X$} . . . { \frac{x+6}{2} = 7 \}

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Introduction

Solving for $x$ in an equation involves isolating the variable $x$ on one side of the equation. In this case, we are given the equation $\frac{x+6}{2} = 7$, and we need to solve for $x$. This equation involves a fraction, and we will need to use algebraic techniques to isolate $x$.

Step 1: Multiply Both Sides by 2

To eliminate the fraction, we can multiply both sides of the equation by 2. This will give us:

$$x+6 = 14$$

Step 2: Subtract 6 from Both Sides

Next, we need to isolate $x$ by subtracting 6 from both sides of the equation. This will give us:

$$x = 8$$

Conclusion

We have now solved for $x$ in the equation $\frac{x+6}{2} = 7$. The value of $x$ is 8.

Example Use Case

Solving for $x$ in an equation is a fundamental concept in algebra and is used in a wide range of applications, including physics, engineering, and economics. For example, if we are given the equation $\frac{x+3}{4} = 5$, we can use the same techniques to solve for $x$.

Step-by-Step Solution

Here is a step-by-step solution to the equation $\frac{x+6}{2} = 7$:

1. Multiply both sides of the equation by 2 to eliminate the fraction.
2. Subtract 6 from both sides of the equation to isolate $x$.
3. The value of $x$ is the result of the equation.

Tips and Tricks

• When solving for $x$ in an equation, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
• If you are given an equation with a fraction, try to eliminate the fraction by multiplying both sides of the equation by the denominator.
• Practice solving for $x$ in different types of equations to become more comfortable with the process.

Common Mistakes

• Failing to follow the order of operations (PEMDAS) when solving for $x$.
• Not eliminating the fraction when given an equation with a fraction.
• Not checking the solution to ensure that it satisfies the original equation.

Real-World Applications

Solving for $x$ in an equation has numerous real-world applications, including:

• Physics: Solving for $x$ is used to calculate distances, velocities, and accelerations in physics problems.
• Engineering: Solving for $x$ is used to design and optimize systems, such as bridges and buildings.
• Economics: Solving for $x$ is used to model economic systems and make predictions about future trends.

Conclusion

Solving for $x$ in an equation is a fundamental concept in algebra that has numerous real-world applications. By following the steps outlined in this article, you can solve for $x$ in a wide range of equations, from simple fractions to more complex equations. With practice and patience, you can become proficient in solving for $x$ and apply this skill to a variety of real-world problems.

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Introduction

Solving for $x$ in an equation involves isolating the variable $x$ on one side of the equation. In this case, we are given the equation $\frac{x+6}{2} = 7$, and we need to solve for $x$. This equation involves a fraction, and we will need to use algebraic techniques to isolate $x$. In this Q&A article, we will answer some common questions related to solving for $x$.

Q: What is the first step in solving for $x$ in an equation?

A: The first step in solving for $x$ in an equation is to eliminate any fractions by multiplying both sides of the equation by the denominator.

Q: How do I eliminate fractions in an equation?

A: To eliminate fractions in an equation, you can multiply both sides of the equation by the denominator. For example, if you have the equation $\frac{x+6}{2} = 7$, you can multiply both sides by 2 to get rid of the fraction.

Q: What is the next step after eliminating fractions?

A: After eliminating fractions, the next step is to isolate $x$ by performing inverse operations. This may involve adding or subtracting numbers from both sides of the equation.

Q: What is the final step in solving for $x$?

A: The final step in solving for $x$ is to check your solution to ensure that it satisfies the original equation.

Q: What if I have a fraction with a variable in the denominator?

A: If you have a fraction with a variable in the denominator, you can multiply both sides of the equation by the variable to eliminate the fraction.

Q: Can I use a calculator to solve for $x$?

A: Yes, you can use a calculator to solve for $x$, but it's essential to understand the steps involved in solving for $x$ so that you can check your solution and ensure that it's correct.

Q: What if I get stuck while solving for $x$?

A: If you get stuck while solving for $x$, try breaking down the problem into smaller steps, and use algebraic techniques to isolate $x$. You can also ask for help from a teacher or tutor.

Q: How do I check my solution to ensure that it satisfies the original equation?

A: To check your solution, substitute the value of $x$ back into the original equation and simplify. If the equation is true, then your solution is correct.

Q: What are some common mistakes to avoid when solving for $x$?

A: Some common mistakes to avoid when solving for $x$ include:

• Failing to follow the order of operations (PEMDAS)
• Not eliminating fractions when necessary
• Not checking the solution to ensure that it satisfies the original equation

Q: Can I use algebraic techniques to solve for $x$ in more complex equations?

A: Yes, you can use algebraic techniques to solve for $x$ in more complex equations, such as quadratic equations or systems of equations.

Q: How do I apply algebraic techniques to solve for $x$ in real-world problems?

A: To apply algebraic techniques to solve for $x$ in real-world problems, you need to understand the context of the problem and use algebraic techniques to model the situation.

Conclusion

Solving for $x$ in an equation is a fundamental concept in algebra that has numerous real-world applications. By following the steps outlined in this article and answering the common questions related to solving for $x$, you can become proficient in solving for $x$ and apply this skill to a variety of real-world problems.