Solving For X: A Step-by-Step Guide To The Equation 2x + 5 = 15

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Hey everyone! Let's dive into a classic math problem and figure out how to solve for x in the equation 2x + 5 = 15. It's a fundamental concept in algebra, and understanding it opens the door to solving way more complex equations. Don't worry; it's easier than it might seem at first glance. We'll break it down step by step, making sure you understand each move.

This equation, 2x + 5 = 15, is a simple linear equation, meaning the highest power of our variable x is 1. Our goal is to isolate x on one side of the equation to find its value. Think of it like a balancing act; whatever we do to one side, we must do to the other to keep things fair. The correct answer from the options provided is, of course, D) 5. Let's see how we got that!

Step-by-Step Solution

Alright, guys, let's walk through the process. Here's how you solve for x in the equation 2x + 5 = 15:

  1. Isolate the term with x: Our first move is to get the term containing x (which is 2x) by itself on one side of the equation. To do this, we need to eliminate the '+ 5' on the left side. We achieve this by subtracting 5 from both sides of the equation. This is a crucial step in maintaining the equation's balance. If we only subtracted 5 from one side, we'd be changing the equation, and our answer wouldn't be valid. So, we perform the same operation on both sides to keep everything equal. This ensures that the equality of the equation is preserved throughout the process. This keeps the equation's integrity intact. The new equation is then 2x + 5 - 5 = 15 - 5. The math becomes quite simple: 2x = 10.

  2. Solve for x: Now we have 2x = 10. This means '2 times x' equals 10. To find the value of a single x, we need to get rid of the '2' that's multiplying it. We do this by dividing both sides of the equation by 2. Again, remember the golden rule: whatever we do to one side, we must do to the other. So, we divide both sides by 2. This gives us (2x) / 2 = 10 / 2. Performing the division, we get x = 5. Congratulations! We've solved for x!

Therefore, x equals 5. From the provided choices, the correct answer is B) 5.

Justification

Let's justify our answer. When we solve for x in the equation 2x + 5 = 15, we arrive at x = 5. To justify this, let's substitute 5 into the original equation and see if it holds true. This substitution confirms the validity of our solution and ensures we haven't made any calculation errors along the way. By plugging 5 into the original equation, we can definitively show if our solution is correct.

Substituting x = 5 into the original equation: 2(5) + 5 = 15.

Let's work through this: 2 times 5 equals 10. So, the equation becomes 10 + 5 = 15.

And, of course, 10 + 5 equals 15. So the equation is balanced: 15 = 15.

This confirms that x = 5 is indeed the correct solution. The equation holds true with x = 5, proving that our calculation is accurate. This step provides assurance that our solution is not only correct but also consistent with the original equation. This verification is a standard practice in mathematics to guarantee the accuracy of the solutions.

Why Understanding This Matters

Understanding how to solve for x is a cornerstone of algebra and higher-level math concepts. It's the foundation for tackling more complex equations and problems. It opens up a world of possibilities! It's not just about passing a math test; it's about developing critical thinking and problem-solving skills that can be applied in various areas of life. This skill is a building block for more advanced mathematical concepts. This approach not only solidifies the concept of solving algebraic equations but also enhances problem-solving abilities overall.

This fundamental skill empowers you to approach complex problems confidently. This process of simplification and isolation of variables is applicable far beyond math. These skills are crucial for navigating various situations and solving intricate problems efficiently. So, keep practicing, and you will become a pro in no time!

Common Mistakes and How to Avoid Them

Even the best of us make mistakes sometimes. When solving for x, here are some common pitfalls and how to avoid them:

  • Not performing the same operation on both sides: This is the most common mistake. Always remember the golden rule. If you subtract, add, multiply, or divide on one side, you must do the same on the other side to keep the equation balanced. If you don't, you'll change the equation and get the wrong answer. Always maintain the equation's equilibrium by applying identical operations on both sides. This balance is fundamental to achieving a correct solution. Keep it in mind, and you're on your way to success.
  • Forgetting the order of operations: Remember PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). Solve in the correct order to get the right answer. Make sure you follow this sequence to ensure you arrive at the correct solution. Following the order of operations ensures the correct execution of mathematical calculations, thereby guaranteeing the accuracy of the results.
  • Making calculation errors: Double-check your work! Simple arithmetic errors can throw off your entire solution. Take your time, and if needed, use a calculator to verify your calculations. Double-checking eliminates calculation mistakes, ensuring a precise solution. Always take the time to verify your work, reducing the chance of error and increasing the reliability of your answer.
  • Not simplifying properly: Always simplify fractions and reduce the expression to its simplest form. This makes it easier to understand and reduces the chances of error. Always make it a habit to simplify your solutions to ensure they are presented in the most concise and comprehensible way possible. This practice enhances accuracy and understanding.

By being aware of these common mistakes, you can avoid them and solve equations more accurately. Practice makes perfect, and the more you work through these problems, the better you'll become.

Conclusion

So, there you have it! Solving for x in the equation 2x + 5 = 15 is a straightforward process once you understand the steps. Remember to isolate the x term, solve for x, and always check your answer. Keep practicing, and you'll build a strong foundation in algebra. You got this! Remember, math is a skill that improves with practice. Keep at it, and you'll master it. This is just the beginning of your mathematical journey! You are doing great!