Write An Equation That Has 18 As A Solution. Show How You Know That 18 Is A Solution.Which Equation Has 18 As A Solution?A. $c + 30 = 48$B. $c + 30 = 55$C. $c + 30 = 50$

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. When we are given an equation and a solution, we can use this information to determine the correct equation. In this article, we will explore how to write an equation that has 18 as a solution and show how we know that 18 is a solution.

Understanding the Problem

To start, let's consider the problem: we need to find an equation that has 18 as a solution. This means that when we substitute 18 into the equation, it should be true. In other words, the equation should be satisfied when c = 18.

Analyzing the Options

We are given three options:

A. c+30=48c + 30 = 48 B. c+30=55c + 30 = 55 C. c+30=50c + 30 = 50

To determine which equation has 18 as a solution, we need to substitute 18 into each option and see which one is true.

Substituting 18 into Each Option

Let's start with option A:

c+30=48c + 30 = 48

Substituting 18 into this equation, we get:

18+30=4818 + 30 = 48

Simplifying this expression, we get:

48=4848 = 48

This equation is true, which means that option A has 18 as a solution.

Checking the Other Options

Now, let's check the other options:

B. c+30=55c + 30 = 55

Substituting 18 into this equation, we get:

18+30=5518 + 30 = 55

Simplifying this expression, we get:

48≠5548 ≠ 55

This equation is false, which means that option B does not have 18 as a solution.

C. c+30=50c + 30 = 50

Substituting 18 into this equation, we get:

18+30=5018 + 30 = 50

Simplifying this expression, we get:

48≠5048 ≠ 50

This equation is false, which means that option C does not have 18 as a solution.

Conclusion

Based on our analysis, we can conclude that option A has 18 as a solution. When we substitute 18 into this equation, it is true. Therefore, the correct equation is:

c+30=48c + 30 = 48

Why 18 is a Solution

So, why is 18 a solution to this equation? To understand this, let's think about what it means for an equation to be true. When we substitute a value into an equation, we are essentially asking whether the equation is satisfied for that value. In this case, we are asking whether the equation c+30=48c + 30 = 48 is satisfied when c = 18.

To see why this is true, let's think about what it means for the equation to be satisfied. The equation is satisfied when the left-hand side (LHS) is equal to the right-hand side (RHS). In this case, the LHS is c+30c + 30 and the RHS is 48.

When c = 18, the LHS becomes:

18+30=4818 + 30 = 48

This expression is equal to the RHS, which is 48. Therefore, the equation is satisfied when c = 18, which means that 18 is a solution to the equation.

Key Takeaways

In this article, we have learned how to write an equation that has 18 as a solution and show how we know that 18 is a solution. We have also analyzed three options and determined that option A has 18 as a solution.

Here are the key takeaways:

  • To write an equation that has 18 as a solution, we need to find an equation that is satisfied when c = 18.
  • We can substitute 18 into each option and see which one is true.
  • The correct equation is c+30=48c + 30 = 48.
  • 18 is a solution to this equation because the LHS is equal to the RHS when c = 18.

Final Thoughts

Q: What is a solution to an equation?

A: A solution to an equation is a value that makes the equation true. In other words, when we substitute a solution into an equation, the equation is satisfied.

Q: How do I know if a value is a solution to an equation?

A: To determine if a value is a solution to an equation, we need to substitute the value into the equation and see if it is true. If the equation is satisfied, then the value is a solution.

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

A: A variable is a letter or symbol that represents a value, while a solution is a specific value that makes the equation true. In other words, a variable is a placeholder for a value, while a solution is the actual value that makes the equation true.

Q: Can a value be a solution to more than one equation?

A: Yes, a value can be a solution to more than one equation. For example, the value 2 is a solution to the equation x + 2 = 4, but it is also a solution to the equation x + 2 = 6.

Q: How do I write an equation that has a given solution?

A: To write an equation that has a given solution, we need to find an equation that is satisfied when the solution is substituted into it. We can do this by using the solution to create an equation that is true.

Q: What is the process for solving equations with given solutions?

A: The process for solving equations with given solutions involves the following steps:

  1. Read the problem and understand what is being asked.
  2. Identify the given solution and the equation that needs to be satisfied.
  3. Substitute the solution into the equation and see if it is true.
  4. If the equation is satisfied, then the solution is correct.
  5. If the equation is not satisfied, then the solution is incorrect.

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

A: Some common mistakes to avoid when solving equations with given solutions include:

  • Not reading the problem carefully and understanding what is being asked.
  • Not identifying the given solution and the equation that needs to be satisfied.
  • Not substituting the solution into the equation correctly.
  • Not checking if the equation is satisfied after substituting the solution.

Q: How can I practice solving equations with given solutions?

A: There are many ways to practice solving equations with given solutions, including:

  • Working through practice problems in a textbook or online resource.
  • Creating your own practice problems and solving them.
  • Asking a teacher or tutor for help and guidance.
  • Joining a study group or working with a partner to practice solving equations with given solutions.

Q: What are some real-world applications of solving equations with given solutions?

A: Solving equations with given solutions has many real-world applications, including:

  • Science: Solving equations with given solutions is used to model real-world phenomena, such as the motion of objects or the behavior of chemical reactions.
  • Engineering: Solving equations with given solutions is used to design and optimize systems, such as bridges or electronic circuits.
  • Economics: Solving equations with given solutions is used to model economic systems and make predictions about future trends.
  • Computer Science: Solving equations with given solutions is used to develop algorithms and solve problems in computer science.

Conclusion

Solving equations with given solutions is an important concept in mathematics that has many real-world applications. By understanding how to write an equation that has a given solution and show how we know that the solution is correct, we can better understand the properties of equations and how to solve them. We hope that this article has been helpful in understanding this concept and that you will continue to explore and learn more about mathematics.