The Solutions Of The Following Three Equations Are 9, 10, And 12, But Not Necessarily In That Order. Use Substitution To Match Each Equation With The Correct Solution.1. $x + 6 = 18$2. $2x = 18$3. 14 = X + 4 14 = X + 4 14 = X + 4

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Introduction

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In this article, we will explore the solutions of three given equations and use substitution to match each equation with the correct solution. The solutions provided are 9, 10, and 12, but not necessarily in that order. We will use algebraic manipulation and substitution to determine the correct equation for each solution.

Equation 1: $x + 6 = 18$

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The first equation is $x + 6 = 18$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. We can do this by subtracting 6 from both sides of the equation.

Step 1: Subtract 6 from both sides

x + 6 = 18
x + 6 - 6 = 18 - 6
x = 12

The solution to the first equation is $x = 12$. However, we are given that the solution is either 9, 10, or 12. Since we have found that the solution is 12, we can conclude that the first equation is $x + 6 = 18$.

Equation 2: $2x = 18$

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The second equation is $2x = 18$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. We can do this by dividing both sides of the equation by 2.

Step 1: Divide both sides by 2

2x = 18
(2x) / 2 = 18 / 2
x = 9

The solution to the second equation is $x = 9$. Since we have found that the solution is 9, we can conclude that the second equation is $2x = 18$.

Equation 3: $14 = x + 4$

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The third equation is $14 = x + 4$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. We can do this by subtracting 4 from both sides of the equation.

Step 1: Subtract 4 from both sides

14 = x + 4
14 - 4 = x + 4 - 4
10 = x

The solution to the third equation is $x = 10$. Since we have found that the solution is 10, we can conclude that the third equation is $14 = x + 4$.

Conclusion

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In this article, we have used substitution to match each equation with the correct solution. We have found that the first equation is $x + 6 = 18$, the second equation is $2x = 18$, and the third equation is $14 = x + 4$. The solutions to the equations are 12, 9, and 10, respectively.

Final Answer

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The final answer is:

• Equation 1: $x + 6 = 18$ with solution $x = 12$
• Equation 2: $2x = 18$ with solution $x = 9$
• Equation 3: $14 = x + 4$ with solution $x = 10$
  

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Introduction

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In our previous article, we explored the solutions of three given equations and used substitution to match each equation with the correct solution. In this article, we will answer some frequently asked questions related to the solutions of the three equations.

Q: What is the process of substitution in solving equations?

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A: The process of substitution in solving equations involves replacing one variable with an expression that is equal to the other variable. This is done to simplify the equation and solve for the variable.

Q: How do you use substitution to solve the equation $x + 6 = 18$?

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A: To use substitution to solve the equation $x + 6 = 18$, we need to isolate the variable $x$ on one side of the equation. We can do this by subtracting 6 from both sides of the equation, which gives us $x = 12$.

Q: What is the solution to the equation $2x = 18$?

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A: The solution to the equation $2x = 18$ is $x = 9$. We can find this solution by dividing both sides of the equation by 2.

Q: How do you use substitution to solve the equation $14 = x + 4$?

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A: To use substitution to solve the equation $14 = x + 4$, we need to isolate the variable $x$ on one side of the equation. We can do this by subtracting 4 from both sides of the equation, which gives us $x = 10$.

Q: What is the relationship between the solutions of the three equations?

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A: The solutions of the three equations are related in that they are all different values of the variable $x$. The first equation has a solution of $x = 12$, the second equation has a solution of $x = 9$, and the third equation has a solution of $x = 10$.

Q: How do you determine which equation corresponds to which solution?

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A: To determine which equation corresponds to which solution, we need to use substitution to solve each equation and compare the solutions to the given solutions. In this case, we found that the first equation corresponds to the solution $x = 12$, the second equation corresponds to the solution $x = 9$, and the third equation corresponds to the solution $x = 10$.

Q: What is the importance of using substitution in solving equations?

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A: The importance of using substitution in solving equations is that it allows us to simplify the equation and solve for the variable. This is especially useful when the equation is complex or when we need to find the solution to a system of equations.

Q: Can you provide an example of a system of equations that can be solved using substitution?

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A: Yes, here is an example of a system of equations that can be solved using substitution:

Equation 1: $x + 2y = 6$ Equation 2: $2x - 3y = -3$

We can solve this system of equations by using substitution to solve for one variable in terms of the other variable. For example, we can solve 1 for $x$ in terms of $y$ and then substitute this expression into Equation 2.

Conclusion

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In this article, we have answered some frequently asked questions related to the solutions of the three equations. We have discussed the process of substitution in solving equations, how to use substitution to solve the three equations, and the relationship between the solutions of the three equations. We have also provided an example of a system of equations that can be solved using substitution.

Final Answer

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The final answer is:

• Equation 1: $x + 6 = 18$ with solution $x = 12$
• Equation 2: $2x = 18$ with solution $x = 9$
• Equation 3: $14 = x + 4$ with solution $x = 10$