Solving For 'e': A Simple Math Equation Explained

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Solving for 'e': A Simple Math Equation Explained

Hey math enthusiasts! Today, we're diving into a straightforward algebraic equation: 150 = e + 42. Our goal? To solve for 'e', which means figuring out the value of the unknown variable 'e' that makes this equation true. Don't worry, it's not as scary as it sounds! We'll break it down step-by-step, making sure everyone, from math newbies to seasoned pros, can follow along. This equation is a fantastic example of a basic algebraic problem, and understanding how to solve it is a fundamental skill in mathematics. By the end of this guide, you'll not only know how to solve this specific equation but also grasp the underlying principles that apply to a wide range of similar problems. Get ready to flex those brain muscles! Understanding the concept of variables and the basic principles of algebra is key to solving this. Let's get started and make math fun!

The Basics of Equations

First things first, let's talk about what an equation actually is. In math, an equation is a statement that two expressions are equal. Think of it like a balanced scale; whatever you do to one side, you have to do to the other to keep it balanced. The equal sign (=) is the heart of the equation, showing that the value on the left side is the same as the value on the right side. In our equation, 150 = e + 42, the expression on the left is 150, and the expression on the right is e + 42. Our mission is to find the value of 'e' that makes the scale perfectly balanced. This involves isolating 'e' on one side of the equation. To do this, we'll use the principles of inverse operations. Inverse operations are operations that undo each other. For example, addition and subtraction are inverse operations. Multiplication and division are also inverse operations. Understanding these inverse operations is the key to solving most algebraic equations. When we manipulate an equation, we must apply the same operation to both sides to maintain the equality. It's like a seesaw; if you add weight to one side, you must add the same weight to the other side to keep it balanced. This ensures that the equation remains valid throughout the solving process. Let's use this understanding to solve our specific equation, 150 = e + 42, step by step.

Step-by-Step Solution

Now, let's dive into solving the equation 150 = e + 42. Remember, our goal is to isolate 'e' on one side of the equation. We do this by getting rid of the + 42 on the right side. The principle is simple: use inverse operations. Since we have + 42, we need to subtract 42 from both sides of the equation. This is where the magic happens! Here's how it looks:

  1. Original Equation: 150 = e + 42
  2. Subtract 42 from both sides: 150 - 42 = e + 42 - 42
  3. Simplify: 108 = e

And there you have it! We've solved for 'e'. The value of 'e' that makes the equation true is 108. Now, let's double-check our work to make sure we got it right. Substituting 108 back into the original equation, we get 150 = 108 + 42. Does this add up? Yep, it does! 108 + 42 equals 150, confirming that our answer is correct. This process of checking your answer is crucial in algebra. It helps you catch any mistakes you might have made during the solving process. It's always a good habit to verify your solutions. This simple check gives you confidence in your answer and reinforces your understanding of the equation. Knowing how to solve these problems is useful for a variety of purposes. The ability to manipulate and solve equations is a fundamental skill that applies to many areas of mathematics and science. Congratulations, you've successfully solved for 'e'! The steps we took, subtracting from both sides, are the foundation of many algebraic solutions.

Why This Matters: Real-World Applications

So, why does solving for 'e' matter, and how can you use this in the real world? While this specific equation might not pop up in your daily life, the principles behind it are incredibly useful. The core concept of solving for an unknown variable is essential in various fields. Imagine you're managing a budget. You know your total income and some of your expenses, but you want to calculate how much you have left for savings. This is an equation in disguise! Or, think about a construction project where you need to calculate the length of a missing side of a building, given other dimensions and the total area. It’s all about finding the missing piece of the puzzle. The ability to solve these simple equations translates directly into the ability to solve more complex problems in the future. In fields like physics, chemistry, engineering, and computer science, solving equations is a daily activity. From calculating forces to analyzing data, these skills are fundamental. Even in everyday situations, such as figuring out the cost of multiple items or determining the amount of ingredients needed for a recipe, these basic mathematical skills come in handy. It’s like having a superpower that lets you understand and manipulate numbers to solve all kinds of problems. This foundational knowledge is crucial as you move on to more advanced math concepts.

Further Practice and Resources

Want to sharpen your skills? Great! Here are a few exercises to get you going and resources to help you along the way. Practicing is key to mastering any new skill. The more problems you solve, the more comfortable and confident you'll become. Here are some practice problems similar to the one we just solved:

  1. Solve for x: 75 = x + 25
  2. Solve for y: 200 = y + 80
  3. Solve for z: 50 = z + 10

Try these problems on your own, and then check your answers. Remember to always double-check your work to make sure your solutions are correct. If you get stuck, don’t worry! Just go back through the steps we covered, and you'll find the answer. For extra help, here are some resources:

  • Khan Academy: A fantastic free resource with videos and practice exercises on algebra.
  • Mathway: An online calculator that can solve equations and show you the steps.
  • Your textbook or online math resources: Many textbooks and websites offer additional practice problems and explanations.

Keep practicing, and you'll become a pro at solving these types of equations in no time! Keep in mind that math is all about practice and repetition. The more you work at it, the easier it becomes. By consistently practicing and using the provided resources, you'll build a strong foundation in algebra. Embrace the challenge, enjoy the process, and watch your skills grow. Happy solving!