How Many Solutions Exist For The Given Equation?${3x + 13 = 3(x + 6) + 1}$A. Zero B. One C. Infinitely Many D. Two

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Introduction

In mathematics, equations are a fundamental concept that help us understand the relationship between variables. When we are given an equation, our goal is to find the solution or the value of the variable that satisfies the equation. In this article, we will explore the given equation: 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1. Our objective is to determine the number of solutions that exist for this equation.

Understanding the Equation

The given equation is a linear equation, which means it can be written in the form ax+b=cax + b = c. In this case, the equation is 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1. To solve this equation, we need to simplify it and isolate the variable xx.

Simplifying the Equation

To simplify the equation, we can start by expanding the right-hand side using the distributive property. This gives us:

3x+13=3x+18+13x + 13 = 3x + 18 + 1

Next, we can combine like terms on the right-hand side:

3x+13=3x+193x + 13 = 3x + 19

Isolating the Variable

Now that we have simplified the equation, we can isolate the variable xx by subtracting 3x3x from both sides:

13=1913 = 19

However, this is not a valid equation, as the left-hand side is a constant and the right-hand side is an expression that depends on xx. This means that the equation has no solution.

Conclusion

In conclusion, the given equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 has no solution. This is because the equation is inconsistent, meaning that it is impossible to find a value of xx that satisfies the equation.

Why is the Equation Inconsistent?

The equation is inconsistent because the left-hand side and the right-hand side are not equal. The left-hand side is a constant, while the right-hand side is an expression that depends on xx. This means that there is no value of xx that can make the two sides equal.

What is the Implication of an Inconsistent Equation?

An inconsistent equation has no solution, which means that it is impossible to find a value of xx that satisfies the equation. This can be a problem in many areas of mathematics and science, as it can lead to incorrect conclusions and solutions.

How to Avoid Inconsistent Equations

To avoid inconsistent equations, it is essential to carefully check the equation for any errors or inconsistencies. This can be done by simplifying the equation and checking if the left-hand side and the right-hand side are equal.

Conclusion

In conclusion, the given equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 has no solution. This is because the equation is inconsistent, meaning that it is impossible to find a value of xx that satisfies the equation. By carefully checking the equation and simplifying it, we can avoid inconsistent equations and find the correct solution.

Final Answer

The final answer is A. Zero.

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Q: What is the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 trying to solve?

A: The equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 is trying to find the value of the variable xx that satisfies the equation.

Q: Why is the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 inconsistent?

A: The equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 is inconsistent because the left-hand side and the right-hand side are not equal. The left-hand side is a constant, while the right-hand side is an expression that depends on xx.

Q: What is the implication of an inconsistent equation?

A: An inconsistent equation has no solution, which means that it is impossible to find a value of xx that satisfies the equation. This can be a problem in many areas of mathematics and science, as it can lead to incorrect conclusions and solutions.

Q: How to avoid inconsistent equations?

A: To avoid inconsistent equations, it is essential to carefully check the equation for any errors or inconsistencies. This can be done by simplifying the equation and checking if the left-hand side and the right-hand side are equal.

Q: What is the difference between a consistent and an inconsistent equation?

A: A consistent equation is one that has a solution, while an inconsistent equation is one that has no solution. In other words, a consistent equation is one that can be solved, while an inconsistent equation is one that cannot be solved.

Q: Can an inconsistent equation be solved?

A: No, an inconsistent equation cannot be solved. This is because the equation is impossible to satisfy, and there is no value of xx that can make the two sides equal.

Q: What is the final answer to the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1?

A: The final answer to the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 is A. Zero.

Q: Why is the final answer A. Zero?

A: The final answer A. Zero is because the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 is inconsistent, meaning that it has no solution. Therefore, the final answer is A. Zero.

Q: Can I use the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 in a real-world application?

A: No, the equation 3x+13=3(x+6)+13x + 13 = 3(x + 6) + 1 is not suitable for real-world applications because it is inconsistent and has no solution. Inconsistent equations can lead to incorrect conclusions and solutions, which can be a problem in many areas of mathematics and science.

Q: How to determine if an equation is consistent or inconsistent?

A: To determine if an equation is consistent or inconsistent, you can simplify the equation and check if the left-hand side and the right-hand side are equal. If they are equal, then the equation is consistent. If they are not equal, then the equation is inconsistent.

Q: What is the importance of checking for consistency in equations?

A: Checking for consistency in equations is essential because it can help you avoid incorrect conclusions and solutions. Inconsistent equations can lead to problems in many areas of mathematics and science, so it is crucial to check for consistency before using an equation in a real-world application.