Solve For \[$ X \$\]:$\[ 14x = 91 \\]

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Introduction

Solving for $x$ in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a linear equation. In this discussion, we will focus on solving for $x$ in the equation $14x = 91$. This equation is a simple linear equation, and we will use the basic algebraic properties to isolate the variable $x$.

Understanding the Equation

The given equation is $14x = 91$. This equation states that the product of $14$ and $x$ is equal to $91$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. In this case, we can start by dividing both sides of the equation by $14$.

Isolating the Variable

To isolate the variable $x$, we can use the following steps:

1. Divide both sides of the equation by $14$.
2. Simplify the equation to get the value of $x$.

Using the above steps, we can rewrite the equation as follows:

$$\frac{14x}{14} = \frac{91}{14}$$

Simplifying the Equation

Now, we can simplify the equation by canceling out the common factor of $14$ on both sides of the equation.

$$x = \frac{91}{14}$$

Evaluating the Expression

To evaluate the expression $\frac{91}{14}$, we can divide $91$ by $14$.

$$x = 6.5$$

Conclusion

In this discussion, we solved for $x$ in the equation $14x = 91$. We used the basic algebraic properties to isolate the variable $x$ on one side of the equation. By dividing both sides of the equation by $14$, we were able to simplify the equation and get the value of $x$. The final answer is $x = 6.5$.

Additional Examples

Here are a few more examples of solving for $x$ in linear equations:

• $3x = 24$
• $2x = 16$
• $5x = 30$

Tips and Tricks

Here are a few tips and tricks to help you solve for $x$ in linear equations:

• Make sure to follow the order of operations (PEMDAS) when simplifying the equation.
• Use the distributive property to expand the equation if necessary.
• Check your answer by plugging it back into the original equation.

Real-World Applications

Solving for $x$ in linear equations has many real-world applications. Here are a few examples:

• In physics, solving for $x$ can help you calculate the position of an object in a given time.
• In finance, solving for $x$ can help you calculate the interest rate on a loan.
• In engineering, solving for $x$ can help you calculate the stress on a material.

Final Thoughts

Solving for $x$ in linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a linear equation. By following the steps outlined in this discussion, you can solve for $x$ in any linear equation. Remember to always check your answer by plugging it back into the original equation, and don't be afraid to ask for help if you get stuck.

Frequently Asked Questions

Here are a few frequently asked questions about solving for $x$ in linear equations:

• Q: What is the first step in solving for $x$ in a linear equation? A: The first step is to isolate the variable $x$ on one side of the equation.
• Q: How do I simplify the equation after isolating the variable? A: You can simplify the equation by canceling out any common factors on both sides of the equation.
• Q: What is the final answer to the equation $14x = 91$? A: The final answer is $x = 6.5$.
  

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Introduction

In our previous discussion, we solved for $x$ in the equation $14x = 91$. We used the basic algebraic properties to isolate the variable $x$ on one side of the equation. In this Q&A article, we will answer some of the most frequently asked questions about solving for $x$ in linear equations.

Q&A

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

A: The first step is to isolate the variable $x$ on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by a constant.

Q: How do I simplify the equation after isolating the variable?

A: You can simplify the equation by canceling out any common factors on both sides of the equation. For example, if you have the equation $2x = 12$, you can simplify it by dividing both sides by $2$ to get $x = 6$.

Q: What is the final answer to the equation $14x = 91$?

A: The final answer is $x = 6.5$. This is obtained by dividing both sides of the equation by $14$.

Q: Can I use the same steps to solve for $x$ in a quadratic equation?

A: No, the steps for solving for $x$ in a quadratic equation are different from those for a linear equation. In a quadratic equation, you may need to use the quadratic formula to solve for $x$.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that is used to solve for $x$ in a quadratic equation. The formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q: How do I use the quadratic formula to solve for $x$?

A: To use the quadratic formula, you need to identify the values of $a$, $b$, and $c$ in the quadratic equation. Then, you can plug these values into the formula to solve for $x$.

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 $1$. A quadratic equation is an equation in which the highest power of the variable is $2$.

Q: Can I use a calculator to solve for $x$ in a linear or quadratic equation?

A: Yes, you can use a calculator to solve for $x$ in a linear or quadratic equation. However, it's always a good idea to check your answer by plugging it back into the original equation.

Q: What are some common mistakes to avoid when solving for $x$ in a linear or quadratic equation?

A: Some common mistakes to avoid include:

• Not isolating the variable $x$ on one side of the equation
• Not simplifying the equation after isolating the variable
• Not checking the answer by plugging it back into the original equation
• Not using the correct formula or method to solve for $x$

Conclusion

Solving for $x$ in linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a linear equation. By following the steps outlined in this Q&A article, you can solve for $x$ in any linear equation. Remember to always check your answer by plugging it back into the original equation, and don't be afraid to ask for help if you get stuck.

Additional Resources

Here are some additional resources that you may find helpful:

• Online calculators for solving linear and quadratic equations
• Math textbooks and workbooks for practice problems
• Online math communities and forums for asking questions and getting help
• Math software and apps for solving linear and quadratic equations

Final Thoughts

Solving for $x$ in linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a linear equation. By following the steps outlined in this Q&A article, you can solve for $x$ in any linear equation. Remember to always check your answer by plugging it back into the original equation, and don't be afraid to ask for help if you get stuck.