Solving X In The Equation X/35 = 7

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Finding the unknown variable in an equation is a fundamental skill in mathematics. In this article, we will explore the equation x / 35 = 7 and methodically determine the value of x. This is a crucial concept that underpins various mathematical and real-world applications. Understanding how to solve for x in such equations is not only essential for academic success but also for practical problem-solving in everyday life. Whether you are a student grappling with algebra or someone looking to brush up on your math skills, this guide will provide you with a clear and concise understanding of the process.

Understanding the Equation

At the heart of this problem is the equation x / 35 = 7. To truly grasp the solution, we need to break down what this equation means. The equation is essentially stating that some number, represented by the variable x, when divided by 35, results in 7. In algebraic terms, this is a simple yet powerful statement that allows us to isolate and determine the value of x. Before we delve into the steps to solve for x, it’s crucial to recognize the relationship between division and multiplication. These two operations are inverse operations, meaning one can undo the other. This inverse relationship is the key to solving equations of this type. Understanding this concept forms the bedrock of solving various algebraic problems and equations, making it an indispensable tool in mathematics.

Isolating the Variable x

The primary goal in solving any algebraic equation is to isolate the variable. In our case, we want to find x, so we need to get x alone on one side of the equation. The equation x / 35 = 7 tells us that x is being divided by 35. To undo this division, we use the inverse operation: multiplication. The strategy here is to multiply both sides of the equation by 35. This is a critical step because it maintains the balance of the equation. Whatever operation we perform on one side, we must also perform on the other side to ensure the equality remains valid. By multiplying both sides by 35, we effectively cancel out the division on the left side, leaving x isolated. This technique is a cornerstone of algebraic manipulation and is used extensively in solving more complex equations as well. It's a fundamental principle that helps simplify equations and bring us closer to finding the value of the unknown variable.

Step-by-Step Solution

To solve the equation x / 35 = 7, we follow these steps:

  1. Multiply both sides by 35: This is the crucial step to isolate x. By multiplying both sides of the equation by 35, we maintain the balance and work towards getting x by itself.

    • (x / 35) * 35 = 7 * 35

  2. Simplify the left side: On the left side, the multiplication by 35 cancels out the division by 35, leaving us with just x. This is the result of using inverse operations, where multiplication undoes division.

    • x = 7 * 35

  3. Calculate the right side: Now, we multiply 7 by 35 to find the value of the right side of the equation. This multiplication gives us the numerical value that x is equal to.

    • x = 245

  4. Solution: Therefore, the value of x is 245. This is the answer we were seeking, the number that, when divided by 35, equals 7. This step-by-step approach not only solves the equation but also reinforces the process of algebraic problem-solving, which involves isolating the variable through inverse operations.

Verifying the Solution

After finding the solution, it’s always a good practice to verify it. This ensures that our calculations are correct and that the value we found for x indeed satisfies the original equation. To verify our solution, we substitute the value of x back into the original equation: x / 35 = 7. If the equation holds true after the substitution, then our solution is correct. Verification not only confirms the accuracy of the solution but also deepens our understanding of the equation and the problem-solving process. It's a crucial step in mathematical problem-solving that builds confidence and reinforces the concepts learned.

Substituting x = 245

Let’s substitute x = 245 into the original equation:

  • 245 / 35 = 7

Dividing 245 by 35, we get:

  • 7 = 7

Since both sides of the equation are equal, our solution is correct. This confirms that 245 is indeed the value of x that satisfies the equation x / 35 = 7. Verification is a valuable step that helps avoid errors and reinforces the understanding of the mathematical concepts involved.

Answer Choices and the Correct Option

Now that we have solved for x and verified the solution, let’s consider the answer choices provided:

A. 245 B. 7 C. 35 D. 5

Our solution, x = 245, matches answer choice A. Therefore, the correct answer is A. This step is crucial in multiple-choice questions, where identifying the correct option from a list is the final step in the problem-solving process. It requires not only solving the equation accurately but also matching the solution with the given options.

Conclusion

In summary, to solve the equation x / 35 = 7, we used the principle of inverse operations. We multiplied both sides of the equation by 35 to isolate x, resulting in x = 245. We then verified our solution by substituting x = 245 back into the original equation, confirming its accuracy. This step-by-step approach illustrates a fundamental method for solving algebraic equations. Understanding how to isolate variables and use inverse operations is a cornerstone of algebra and mathematics in general. This skill is not only essential for academic pursuits but also for practical problem-solving in various real-life situations. By mastering these techniques, you build a strong foundation for tackling more complex mathematical challenges and develop critical thinking skills that are applicable across different domains.

Mastering basic algebraic equations like x / 35 = 7 is a stepping stone to more advanced mathematical concepts. The ability to confidently solve for unknowns is a skill that extends beyond the classroom, finding applications in various fields such as science, engineering, finance, and even everyday decision-making. By understanding the principles of algebra, you empower yourself with a powerful tool for problem-solving and analytical thinking. This foundation enables you to approach complex challenges with a systematic and logical mindset, breaking down problems into manageable steps and arriving at accurate solutions. As you continue your mathematical journey, remember that each equation solved and each concept mastered contributes to a deeper understanding of the world around you.