Solving For X In X/2 = 17 A Step-by-Step Guide

Detailed Solution and Explanation

The question asks us to solve for x in the equation x / 2 = 17. This is a fundamental algebraic problem that can be solved by applying the basic principles of equation manipulation. The core concept here is to isolate the variable x on one side of the equation. To do this, we need to undo the operation that is being applied to x, which in this case is division by 2. The inverse operation of division is multiplication. Therefore, to isolate x, we need to multiply both sides of the equation by 2. Multiplying both sides of the equation by 2 ensures that we maintain the equality. This is a crucial principle in algebra: whatever operation we perform on one side of the equation, we must also perform on the other side to keep the equation balanced. Let's perform the multiplication: (x / 2) * 2 = 17 * 2. On the left side, the multiplication by 2 cancels out the division by 2, leaving us with just x. On the right side, 17 multiplied by 2 equals 34. Therefore, the equation simplifies to x = 34. This is our solution. We have successfully isolated x and found its value. However, it's always a good practice to verify our solution to ensure its accuracy. To do this, we substitute the value of x back into the original equation and check if it holds true. In this case, we substitute x = 34 into the equation x / 2 = 17. This gives us 34 / 2 = 17. Simplifying the left side, we get 17 = 17, which is true. This confirms that our solution, x = 34, is correct. The other options provided are incorrect. Option A, x = 8.5, would give 8. 5 / 2 = 4.25, which is not equal to 17. Option B, x = 15, would give 15 / 2 = 7.5, which is also not equal to 17. Option D, x = 19, would give 19 / 2 = 9.5, which is again not equal to 17. These incorrect options highlight the importance of carefully following the steps of algebraic manipulation and verifying the solution. Understanding the process of solving for x in this equation provides a solid foundation for tackling more complex algebraic problems. The key takeaway is the principle of maintaining balance by performing the same operations on both sides of the equation. This, combined with the understanding of inverse operations, allows us to isolate variables and arrive at accurate solutions. In conclusion, the solution to the equation x / 2 = 17 is x = 34. This was achieved by multiplying both sides of the equation by 2, isolating x, and then verifying the solution by substituting it back into the original equation. This step-by-step approach provides a clear and concise method for solving similar algebraic problems.

Step-by-Step Solution: Finding the Value of x

The problem at hand requires us to solve for x in the equation x / 2 = 17. This is a quintessential example of a linear equation, and solving it involves isolating the variable x on one side of the equation. The equation presents x divided by 2, which equals 17. To isolate x, we need to perform the inverse operation of division, which is multiplication. The fundamental principle in solving algebraic equations is maintaining balance. Whatever operation we perform on one side of the equation, we must also perform on the other side to ensure that the equality holds. In this case, to eliminate the division by 2, we will multiply both sides of the equation by 2. This step is crucial as it effectively undoes the division, allowing us to get x by itself. Let's break down the process step by step: First, we write down the original equation: x / 2 = 17. Next, we multiply both sides of the equation by 2. This gives us: (x / 2) * 2 = 17 * 2. On the left side of the equation, the multiplication by 2 cancels out the division by 2. This leaves us with just x. On the right side of the equation, we have 17 multiplied by 2, which equals 34. So, the equation simplifies to: x = 34. This is our solution. We have successfully isolated x and found its value. However, to ensure the accuracy of our solution, we should always verify it by substituting it back into the original equation. Let's substitute x = 34 into the original equation x / 2 = 17. This gives us: 34 / 2 = 17. Now, we simplify the left side of the equation: 34 divided by 2 is indeed 17. So, we have: 17 = 17. This confirms that our solution, x = 34, is correct. The other answer choices provided are incorrect. Option A, x = 8.5, would give 8. 5 / 2 = 4.25, which is not equal to 17. Option B, x = 15, would give 15 / 2 = 7.5, which is also not equal to 17. Option D, x = 19, would give 19 / 2 = 9.5, which is again not equal to 17. These incorrect options underscore the importance of meticulous algebraic manipulation and solution verification. In summary, solving for x in the equation x / 2 = 17 involves multiplying both sides of the equation by 2 to isolate x. This yields the solution x = 34, which can be verified by substituting it back into the original equation. This step-by-step method provides a clear and reliable approach to solving similar linear equations. Understanding these fundamental algebraic principles is essential for tackling more complex mathematical problems in the future.

Why x = 34 is the Correct Solution

To definitively determine why x = 34 is the correct solution to the equation x / 2 = 17, let's revisit the fundamental principles of solving algebraic equations and dissect the process step by step. The primary goal when solving for a variable in an equation is to isolate that variable on one side of the equation. In other words, we want to manipulate the equation in such a way that x is by itself on one side, with its value on the other side. The equation we are dealing with is x / 2 = 17. This equation states that some number, represented by x, when divided by 2, results in 17. To isolate x, we need to undo the division by 2. The inverse operation of division is multiplication. Therefore, we must multiply both sides of the equation by 2. This is a crucial step, and it's based on the fundamental principle that whatever operation we perform on one side of an equation, we must perform the same operation on the other side to maintain the equality. When we multiply both sides of the equation by 2, we get: (x / 2) * 2 = 17 * 2. On the left side of the equation, the multiplication by 2 cancels out the division by 2. This is because multiplying by 2 is the inverse operation of dividing by 2, and these operations effectively nullify each other. This leaves us with just x on the left side. On the right side of the equation, we have 17 multiplied by 2. Performing this multiplication, we find that 17 * 2 = 34. Therefore, the equation simplifies to: x = 34. This is our solution. We have successfully isolated x and determined its value to be 34. But why are the other options incorrect? Let's examine them: Option A suggests x = 8.5. If we substitute this value back into the original equation, we get 8. 5 / 2 = 4.25, which is not equal to 17. Therefore, x = 8.5 is not the correct solution. Option B suggests x = 15. Substituting this value into the original equation, we get 15 / 2 = 7.5, which is also not equal to 17. Thus, x = 15 is incorrect. Option D suggests x = 19. Substituting this value, we get 19 / 2 = 9.5, which again is not equal to 17. Hence, x = 19 is not the correct solution either. Only when we substitute x = 34 into the original equation do we get a true statement: 34 / 2 = 17. This confirms that x = 34 is indeed the correct solution. The process of solving for x in this equation highlights the importance of understanding inverse operations and maintaining balance in algebraic equations. By performing the same operation on both sides of the equation, we can isolate the variable and determine its value. In conclusion, x = 34 is the correct solution because it is the only value that satisfies the original equation x / 2 = 17. This was determined by multiplying both sides of the equation by 2 to isolate x and then verifying the solution by substitution. Understanding this process is crucial for solving various algebraic problems and building a strong foundation in mathematics.

Common Mistakes to Avoid When Solving for x

When tackling algebraic equations, especially those involving solving for x, it's crucial to be aware of common mistakes that can lead to incorrect solutions. These mistakes often stem from a misunderstanding of fundamental algebraic principles or simple arithmetic errors. By identifying and avoiding these pitfalls, students can significantly improve their accuracy and confidence in solving equations. One of the most common mistakes is failing to maintain balance in the equation. As emphasized earlier, whatever operation is performed on one side of the equation must also be performed on the other side. For instance, in the equation x / 2 = 17, if a student multiplies the left side by 2 but forgets to multiply the right side by 2, they will arrive at an incorrect solution. This imbalance disrupts the equality and leads to a flawed result. Another frequent error is misapplying inverse operations. In the equation x / 2 = 17, the operation being applied to x is division by 2. The inverse operation is multiplication. However, some students may mistakenly attempt to divide both sides by 2, which would further isolate x and lead to an incorrect answer. Understanding the correct inverse operation is crucial for effectively isolating the variable. Arithmetic errors are also a common source of mistakes. Even if the correct algebraic steps are followed, a simple miscalculation can result in an incorrect solution. For example, in the equation x / 2 = 17, after multiplying both sides by 2, a student might incorrectly calculate 17 * 2 as 32 instead of 34. This arithmetic error would lead to the wrong answer. It's essential to double-check calculations to minimize the risk of such errors. Another mistake to watch out for is incorrect substitution during verification. After solving for x, it's always a good practice to substitute the value back into the original equation to check if it holds true. However, if the substitution is done incorrectly, it can lead to a false confirmation of an incorrect solution. For example, if a student mistakenly solves for x and gets x = 30, and then incorrectly substitutes it into the equation as 30 / 3 = 17, they might falsely conclude that their solution is correct. Careful and accurate substitution is vital for verifying solutions. Finally, a lack of attention to detail can also lead to mistakes. This includes overlooking negative signs, misreading the equation, or simply rushing through the steps without proper focus. Algebra requires precision and attention to detail, and even small oversights can have significant consequences on the final answer. To avoid these common mistakes, it's essential to: 1. Understand and apply the principle of maintaining balance in equations. 2. Correctly identify and apply inverse operations. 3. Double-check all arithmetic calculations. 4. Substitute the solution back into the original equation carefully. 5. Pay close attention to detail and avoid rushing through the steps. By being mindful of these common pitfalls and adopting a methodical approach to problem-solving, students can significantly reduce their chances of making mistakes and improve their algebraic skills. In the context of the equation x / 2 = 17, avoiding these mistakes ensures that one correctly arrives at the solution x = 34. This is achieved by multiplying both sides by 2, performing the arithmetic accurately, and verifying the solution by substitution. A thorough understanding of these concepts and a careful approach to problem-solving are key to success in algebra and beyond.

**Therefore, the best answer is C. x=34