Read the equation carefully

Oct 13, 2025 by talynt.org 69 views

Introduction

In mathematics, solving equations is a fundamental concept that helps us understand the relationship between variables and constants. When we are given an equation, we need to determine if a particular value satisfies the equation. In this case, we are asked to find out if $s = 112$ is a solution to the equation $9 = \frac{s}{28}$ . To answer this question, we need to substitute the value of $s$ into the equation and check if it holds true.

Understanding the Equation

The given equation is $9 = \frac{s}{28}$ . This is a simple algebraic equation where we have a fraction on the right-hand side. To solve for $s$ , we need to isolate the variable $s$ on one side of the equation. We can do this by multiplying both sides of the equation by the denominator, which is $28$ .

Solving for $s$

To solve for $s$ , we multiply both sides of the equation by $28$ :

9 \times 28 = \frac{s}{28} \times 28

This simplifies to:

252 = s

Checking if $s = 112$ is a Solution

Now that we have solved for $s$ , we need to check if $s = 112$ is a solution to the equation. We can do this by substituting $s = 112$ into the original equation:

9 = \frac{112}{28}

To simplify this, we can divide $112$ by $28$ :

\frac{112}{28} = 4

Conclusion

As we can see, $4$ is not equal to $9$ , which means that $s = 112$ is not a solution to the equation $9 = \frac{s}{28}$ . Therefore, the correct answer is:

B. No

Why is $s = 112$ not a Solution?

$s = 112$ is not a solution to the equation $9 = \frac{s}{28}$ because it does not satisfy the equation. When we substitute $s = 112$ into the equation, we get $4$ , which is not equal to $9$ . This means that $s = 112$ does not satisfy the equation, and therefore, it is not a solution.

What is the Correct Solution?

To find the correct solution, we need to solve for $s$ using the equation $9 = \frac{s}{28}$ . We can do this by multiplying both sides of the equation by $28$ :

9 \times 28 = \frac{s}{28} \times 28

This simplifies to:

252 = s

Therefore, the correct solution is $s = 252$ .

Importance of Solving Equations

Solving equations is an essential skill in mathematics that helps us understand the relationship between variables and constants. It is used in various fields such as science, engineering, and economics to model real-world problems and make predictions. By solving equations, we can determine the value of unknown variables and make informed decisions.

Tips for Solving Equations

Here are some tips for solving equations:

Read the equation carefully: Before solving the equation, read it carefully to understand what is being asked.
Identify the variable: Identify the variable that you need to solve for.
Use algebraic operations: Use algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable.
Check your solution: Once you have solved for the variable, check your solution by substituting it back into the original equation.

Conclusion

In conclusion, $s = 112$ is not a solution to the equation $9 = \frac{s}{28}$ . To find the correct solution, we need to solve for $s$ using the equation. By following the tips for solving equations, we can determine the value of unknown variables and make informed decisions.

Introduction

In our previous article, we discussed whether $s = 112$ is a solution to the equation $9 = \frac{s}{28}$ . We found that $s = 112$ is not a solution to the equation. In this article, we will answer some frequently asked questions related to solving equations and provide additional tips and resources.

Q&A

Q: What is the correct solution to the equation $9 = \frac{s}{28}$ ?

A: The correct solution to the equation $9 = \frac{s}{28}$ is $s = 252$ .

Q: How do I solve for $s$ in the equation $9 = \frac{s}{28}$ ?

A: To solve for $s$ , you can multiply both sides of the equation by $28$ :

9 \times 28 = \frac{s}{28} \times 28

This simplifies to:

252 = s

Q: What if I have a more complex equation, such as $2x + 5 = 11$ ? How do I solve for $x$ ?

A: To solve for $x$ in the equation $2x + 5 = 11$ , you can first subtract $5$ from both sides of the equation:

2x + 5 - 5 = 11 - 5

This simplifies to:

2x = 6

Next, you can divide both sides of the equation by $2$ :

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

This simplifies to:

x = 3

Q: What if I have a fraction in the equation, such as $\frac{x}{4} = 3$ ? How do I solve for $x$ ?

A: To solve for $x$ in the equation $\frac{x}{4} = 3$ , you can multiply both sides of the equation by $4$ :

\frac{x}{4} \times 4 = 3 \times 4

This simplifies to:

x = 12

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: Make sure to read the equation carefully to understand what is being asked.
Not identifying the variable: Identify the variable that you need to solve for.
Not using algebraic operations correctly: Use algebraic operations such as addition, subtraction, multiplication, and division correctly to isolate the variable.
Not checking your solution: Once you have solved for the variable, check your solution by substituting it back into the original equation.

Tips for Solving Equations

Here are some additional tips for solving equations:

Use a systematic approach: Use a systematic approach to solve equations, such as following the order of operations (PEMDAS).
Check your work: Check your work by substituting your solution back into the original equation.
Use visual aids: Use visual aids such as graphs or charts to help you understand the equation and solve for the variable.
Practice, practice, practice: Practice solving equations to become more confident and proficient.

Resources

Here are some additional resources for solving equations:

Online tutorials: Online tutorials such as Khan Academy and Mathway can provide step-by-step instructions and examples for solving equations.
Textbooks: Textbooks such as "Algebra and Trigonometry" by Michael Sullivan can provide a comprehensive introduction to solving equations.
Online communities: Online communities such as Reddit's r/learnmath can provide a supportive community for asking questions and getting help with solving equations.

Conclusion

In conclusion, solving equations is an essential skill in mathematics that helps us understand the relationship between variables and constants. By following the tips and resources provided in this article, you can become more confident and proficient in solving equations. Remember to read the equation carefully, identify the variable, use algebraic operations correctly, and check your solution. With practice and patience, you can master the art of solving equations.