Seven Times A Number Minus The Number Is -48. Find The Number.A. The Number Is 8B. The Number Is -8C. The Number Is 6
Introduction
Mathematics is a fascinating subject that deals with numbers, quantities, and shapes. It is a fundamental tool used in various fields, including science, engineering, economics, and finance. In this article, we will delve into a simple yet intriguing problem that involves algebraic equations. We will explore the solution to the problem "Seven times a number minus the number is -48. Find the number."
Problem Explanation
The problem states that seven times a number minus the number is equal to -48. We can represent this mathematically as:
7x - x = -48
where x is the unknown number.
Algebraic Manipulation
To solve for x, we can start by simplifying the equation. We can combine like terms by adding x to both sides of the equation:
7x - x + x = -48 + x
This simplifies to:
6x = -48 + x
Isolating the Variable
Next, we can isolate the variable x by subtracting x from both sides of the equation:
6x - x = -48
This simplifies to:
5x = -48
Solving for x
To solve for x, we can divide both sides of the equation by 5:
x = -48 / 5
x = -9.6
Checking the Solution
Let's check our solution by plugging x back into the original equation:
7x - x = -48
7(-9.6) - (-9.6) = -48
-67.2 + 9.6 = -48
-57.6 = -48
This is not true, so our solution is incorrect.
Alternative Solution
Let's try a different approach. We can start by simplifying the equation:
7x - x = -48
This simplifies to:
6x = -48
We can then divide both sides of the equation by 6:
x = -48 / 6
x = -8
Checking the Alternative Solution
Let's check our alternative solution by plugging x back into the original equation:
7x - x = -48
7(-8) - (-8) = -48
-56 + 8 = -48
-48 = -48
This is true, so our alternative solution is correct.
Conclusion
In this article, we explored the solution to the problem "Seven times a number minus the number is -48. Find the number." We started by simplifying the equation and isolating the variable x. We then solved for x and checked our solution by plugging x back into the original equation. Our alternative solution, x = -8, was found to be correct.
Discussion
The problem "Seven times a number minus the number is -48. Find the number" is a simple yet intriguing problem that involves algebraic equations. It requires the student to simplify the equation, isolate the variable, and solve for x. The problem is a great example of how algebraic equations can be used to solve real-world problems.
Related Problems
- 3x + 2 = 14
- 2x - 5 = 11
- x/4 + 2 = 5
These problems involve algebraic equations and require the student to simplify the equation, isolate the variable, and solve for x.
Final Answer
The final answer is:
Introduction
In our previous article, we explored the solution to the problem "Seven times a number minus the number is -48. Find the number." We found that the number is -8. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the problem.
Q&A
Q: What is the problem asking for?
A: The problem is asking for a number such that when seven times the number is subtracted from the number, the result is -48.
Q: How do we simplify the equation?
A: We can simplify the equation by combining like terms. In this case, we can add x to both sides of the equation to get:
6x = -48 + x
Q: How do we isolate the variable x?
A: We can isolate the variable x by subtracting x from both sides of the equation. This gives us:
5x = -48
Q: How do we solve for x?
A: We can solve for x by dividing both sides of the equation by 5. This gives us:
x = -48 / 5
x = -9.6
Q: Why is the solution x = -9.6 incorrect?
A: The solution x = -9.6 is incorrect because when we plug x back into the original equation, we get:
7x - x = -48
7(-9.6) - (-9.6) = -48
-67.2 + 9.6 = -48
-57.6 = -48
This is not true, so our solution is incorrect.
Q: What is the correct solution?
A: The correct solution is x = -8. We can verify this by plugging x back into the original equation:
7x - x = -48
7(-8) - (-8) = -48
-56 + 8 = -48
-48 = -48
This is true, so our solution is correct.
Q: Can you provide more examples of algebraic equations?
A: Yes, here are a few examples of algebraic equations:
- 3x + 2 = 14
- 2x - 5 = 11
- x/4 + 2 = 5
These equations require the student to simplify the equation, isolate the variable, and solve for x.
Q: How do I know if my solution is correct?
A: To verify if your solution is correct, you can plug the value of x back into the original equation. If the equation holds true, then your solution is correct.
Conclusion
In this article, we provided a Q&A section to help clarify any doubts and provide additional information on the problem "Seven times a number minus the number is -48. Find the number." We hope that this Q&A section has been helpful in understanding the problem and its solution.
Related Articles
- [Introduction to Algebraic Equations](link to article)
- [Solving Linear Equations](link to article)
- [Solving Quadratic Equations](link to article)
Final Answer
The final answer is: