Is $r = 111$ A Solution To This Equation?$37 = \frac{r}{3}$A. Yes B. No

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Introduction

In mathematics, solving equations is a fundamental concept that helps us understand the relationship between variables. When given an equation, we need to determine if a specific value satisfies the equation. In this case, we are asked to find out if $r = 111$ is a solution to the equation $37 = \frac{r}{3}$. To answer this question, we need to substitute the value of $r$ into the equation and check if it holds true.

Understanding the Equation

The given equation is $37 = \frac{r}{3}$. This equation states that the value of $r$ divided by 3 is equal to 37. To find the value of $r$, we can multiply both sides of the equation by 3, which gives us $r = 37 \times 3$.

Solving for $r$

To solve for $r$, we can multiply 37 by 3, which gives us $r = 111$. However, we need to check if this value satisfies the original equation.

Checking the Solution

To check if $r = 111$ is a solution to the equation, we can substitute this value into the equation and see if it holds true. Substituting $r = 111$ into the equation $37 = \frac{r}{3}$ gives us $37 = \frac{111}{3}$.

Evaluating the Expression

To evaluate the expression $\frac{111}{3}$, we can divide 111 by 3, which gives us 37. This means that the equation $37 = \frac{r}{3}$ is satisfied when $r = 111$.

Conclusion

In conclusion, $r = 111$ is a solution to the equation $37 = \frac{r}{3}$. This is because when we substitute $r = 111$ into the equation, it holds true. Therefore, the correct answer is A. Yes.

Why is this Important?

Understanding how to solve equations and check solutions is crucial in mathematics. It helps us develop problem-solving skills and critical thinking. In real-life scenarios, being able to solve equations and check solutions can help us make informed decisions and solve complex problems.

Real-World Applications

Solving equations and checking solutions has numerous real-world applications. For example, in physics, we use equations to describe the motion of objects. In economics, we use equations to model the behavior of markets. In computer science, we use equations to optimize algorithms and solve complex problems.

Tips and Tricks

When solving equations and checking solutions, here are some tips and tricks to keep in mind:

• Always read the equation carefully and understand what it is asking.
• Use algebraic manipulations to simplify the equation and solve for the variable.
• Check your solution by substituting the value back into the original equation.
• Use a calculator or computer software to check your solution and verify the result.

Common Mistakes

When solving equations and checking solutions, here are some common mistakes to avoid:

• Not reading the equation carefully and misunderstanding what it is asking.
• Not using algebraic manipulations to simplify the equation and solve for the variable.
• Not checking the solution by substituting the value back into the original equation.
• Not using a calculator or computer software to check the solution and verify the result.

Conclusion

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Introduction

In our previous article, we discussed whether $r = 111$ is a solution to the equation $37 = \frac{r}{3}$. We found that $r = 111$ is indeed a solution to the equation. In this article, we will answer some frequently asked questions related to solving equations and checking solutions.

Q&A

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

A: The first step in solving an equation is to read the equation carefully and understand what it is asking. This involves identifying the variables, constants, and any mathematical operations involved.

Q: How do I simplify an equation?

A: To simplify an equation, you can use algebraic manipulations such as combining like terms, factoring, and canceling out common factors.

Q: What is the difference between a solution and a value?

A: A solution is a value that satisfies the equation, while a value is a specific number that can be substituted into the equation.

Q: How do I check if a solution is correct?

A: To check if a solution is correct, you can substitute the value back into the original equation and see if it holds true.

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

A: Some common mistakes to avoid when solving equations include not reading the equation carefully, not using algebraic manipulations to simplify the equation, and not checking the solution by substituting the value back into the original equation.

Q: Can I use a calculator or computer software to solve equations?

A: Yes, you can use a calculator or computer software to solve equations. However, it's always a good idea to check your solution by hand to ensure that it is correct.

Q: How do I know if an equation has a solution?

A: To determine if an equation has a solution, you can try to solve for the variable using algebraic manipulations. If you are unable to solve for the variable, it may indicate that the equation has no solution.

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, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: Can I solve a quadratic equation using algebraic manipulations?

A: Yes, you can solve a quadratic equation using algebraic manipulations such as factoring, completing the square, and the quadratic formula.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula used to solve quadratic equations. It is given by the equation $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q: Can I use the quadratic formula to solve a linear equation?

A: No, you cannot use the quadratic formula to solve a linear equation. The quadratic formula is specifically designed to solve quadratic equations.

Conclusion

In conclusion, solving equations and checking solutions is a crucial skill in mathematics. By following the tips and tricks outlined above and avoiding common mistakes, we can become proficient in solving equations and checking solutions. If you have any further questions or need additional help, feel free to ask.

Additional Resources

For additional resources and practice problems, check out the following websites:

• Khan Academy: www.khanacademy.org
• Mathway: www.mathway.com
• Wolfram Alpha: www.wolframalpha.com

Practice Problems

Try solving the following practice problems:

1. Solve the equation $2x + 5 = 11$.
2. Check if the solution $x = 3$ is correct for the equation $x^2 + 4x - 5 = 0$.
3. Solve the quadratic equation $x^2 + 2x - 6 = 0$ using the quadratic formula.
4. Check if the solution $x = -2$ is correct for the equation $x^2 - 4x + 4 = 0$.

Conclusion

In conclusion, solving equations and checking solutions is a crucial skill in mathematics. By following the tips and tricks outlined above and avoiding common mistakes, we can become proficient in solving equations and checking solutions. If you have any further questions or need additional help, feel free to ask.