What Is The Solution Of Each Equation?1. $9 + K = 18$A. 18 B. 9 C. 8

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Introduction to Solving Equations

Solving equations is a fundamental concept in mathematics that involves finding the value of a variable that makes the equation true. In this article, we will focus on solving linear equations, which are equations that can be written in the form of ax = b, where a and b are constants and x is the variable. We will use the example of the equation 9 + k = 18 to demonstrate the steps involved in solving an equation.

Step 1: Understand the Equation

The first step in solving an equation is to understand what the equation is asking for. In this case, the equation is 9 + k = 18. This means that we need to find the value of k that makes the equation true.

Step 2: Isolate the Variable

To solve for k, we need to isolate the variable on one side of the equation. In this case, we can start by subtracting 9 from both sides of the equation. This will give us k = 18 - 9.

Step 3: Simplify the Equation

Now that we have k = 18 - 9, we can simplify the equation by evaluating the expression on the right-hand side. 18 - 9 = 9, so we have k = 9.

Step 4: Check the Solution

To make sure that our solution is correct, we can plug it back into the original equation and check if it is true. If we substitute k = 9 into the equation 9 + k = 18, we get 9 + 9 = 18, which is true.

Conclusion

In conclusion, the solution to the equation 9 + k = 18 is k = 9. This is the value of k that makes the equation true.

Frequently Asked Questions

  • What is the solution to the equation 9 + k = 18?
  • The solution to the equation 9 + k = 18 is k = 9.
  • How do I solve an equation?
  • To solve an equation, you need to isolate the variable on one side of the equation and then simplify the equation.

Tips and Tricks

  • When solving an equation, make sure to follow the order of operations (PEMDAS) to simplify the equation.
  • Use inverse operations to isolate the variable on one side of the equation.
  • Check your solution by plugging it back into the original equation.

Real-World Applications

Solving equations is a fundamental concept in mathematics that has many real-world applications. For example, in physics, equations are used to describe the motion of objects and to calculate quantities such as velocity and acceleration. In finance, equations are used to calculate interest rates and to determine the value of investments.

Common Mistakes

  • Not following the order of operations (PEMDAS) when simplifying an equation.
  • Not using inverse operations to isolate the variable on one side of the equation.
  • Not checking the solution by plugging it back into the original equation.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that involves finding the value of a variable that makes the equation true. By following the steps outlined in this article, you can solve equations and apply the concepts to real-world problems.

Final Answer

The final answer is: 9\boxed{9}

Introduction

Solving equations is a fundamental concept in mathematics that involves finding the value of a variable that makes the equation true. In this article, we will answer some of the most frequently asked questions about solving equations.

Q: What is the solution to the equation 9 + k = 18?

A: The solution to the equation 9 + k = 18 is k = 9.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable on one side of the equation and then simplify the equation. You can use inverse operations to isolate the variable.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an equation. The acronym PEMDAS stands for:

  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction

Q: How do I use inverse operations to isolate the variable?

A: To use inverse operations to isolate the variable, you need to perform the opposite operation of the one that is being performed on the variable. For example, if the equation is 2x = 6, you can divide both sides of the equation by 2 to isolate the variable x.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation that can be written in the form of ax = b, where a and b are constants and x is the variable. A quadratic equation is an equation that can be written in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: How do I check my solution to an equation?

A: To check your solution to an equation, you need to plug it back into the original equation and check if it is true.

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

A: Some common mistakes to avoid when solving equations include:

  • Not following the order of operations (PEMDAS)
  • Not using inverse operations to isolate the variable
  • Not checking the solution by plugging it back into the original equation

Q: How do I apply the concepts of solving equations to real-world problems?

A: To apply the concepts of solving equations to real-world problems, you need to identify the variables and constants in the problem and then use the concepts of solving equations to find the value of the variable.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that involves finding the value of a variable that makes the equation true. By following the steps outlined in this article, you can solve equations and apply the concepts to real-world problems.

Final Answer

The final answer is: 9\boxed{9}