Solve For M: Mastering Equations & Finding The Value

October 15, 2025 by TextBrain Team 53 views

Hey math enthusiasts! Today, we're diving into a classic algebra problem that's all about solving equations and finding the value of an expression. Specifically, we're tackling the question: "Jika $m$ memenuhi persamaan $4 - 2m = m + 2$ , maka nilai $3m + 1$ adalah" – which, for those of you who might not speak Bahasa Indonesia, translates to something like, "If $m$ satisfies the equation $4 - 2m = m + 2$ , then the value of $3m + 1$ is..." Let's break this down step-by-step so you can totally nail this type of problem, whether it's for a test, a quiz, or just to flex your math muscles. It is not that hard, you will find it easy to solve with my explanation.

Understanding the Problem: The Equation's Core

First things first, let's make sure we're all on the same page about what the question is asking. We're given an equation: $4 - 2m = m + 2$ . The goal here is to find the value of m that makes this equation true. Once we've got that m value, we're not done yet! We need to substitute it into the expression $3m + 1$ and calculate the final result. Think of it like a two-part mission: First, find m; second, plug it in and solve.

Okay, so why is this important, you ask? Well, equations are the backbone of a ton of real-world applications. From calculating the cost of your shopping cart to figuring out the trajectory of a rocket, understanding how to solve equations is a seriously useful skill. This particular type of problem – a simple linear equation – is a building block for more complex math, so getting comfortable with it now is a smart move. Plus, it's a great opportunity to practice your algebraic manipulation skills, which will come in handy throughout your math journey. Trust me, learning this now will make your future math endeavors way smoother. This is the cornerstone of any mathematician, from basic arithmetic to advanced calculus. Now, let us begin solving the equation.

Step-by-Step Solution: Unraveling the Equation

Alright, let's get down to the nitty-gritty and solve this equation. The key to solving for m is to isolate it on one side of the equation. Here’s how we'll do it, step by step:

Combine m terms: Our equation is $4 - 2m = m + 2$ . To get all the m terms on one side, let's add $2m$ to both sides. This gives us: $4 = 3m + 2$ .
Isolate the m term: Next, we need to get the m term by itself. Let's subtract $2$ from both sides of the equation. This yields: $4 - 2 = 3m$ , which simplifies to $2 = 3m$ .
Solve for m: Finally, to find the value of m, we need to divide both sides of the equation by $3$ . So, $m = 2/3$ . We've done it! We have successfully isolated m.

Now, for those of you who prefer a more visual approach, you can think of it like balancing a seesaw. The equation is like the seesaw, and we want to keep it balanced. Every time we do something to one side (like adding or subtracting), we have to do the same thing to the other side to keep it balanced. This ensures that the equation remains true throughout the process. Make sure to double-check your work at each step. This habit can save you from a lot of unnecessary headaches later on. Remember, practice makes perfect, and the more you practice these steps, the faster and more confident you'll become.

Calculating the Final Value: Plugging in the Solution

Now that we've found the value of m (which is 2/3), it's time to plug it into the expression $3m + 1$ and find the final answer. This is where we bring it all together. Let’s substitute $m = 2/3$ into the expression:

Substitute: Replace m with $2/3$ : $3 * (2/3) + 1$ .
Simplify: Multiply $3$ by $2/3$ . The $3$ s cancel out, leaving us with $2$ . So, we have: $2 + 1$ .
Calculate: Add $2$ and $1$ : $2 + 1 = 3$ . Therefore, the value of $3m + 1$ is $3$ when $m = 2/3$ .

So, the correct answer to the question is B. 3. Wasn't that fun? We’ve not only solved the equation but also found the value of the expression, completing the entire problem from start to finish. This process of solving for a variable and then substituting it into an expression is a fundamental concept in algebra, so you've just strengthened your core math skills. Now, let us go deeper into this topic. It is not that hard, as long as you keep practicing, you will become a master of mathematics!

Further Exploration: Expanding Your Math Horizons

This is just one type of problem, but there are many variations on this theme. Let's explore some ways to expand your understanding:

Different Equation Types: Practice solving other types of equations, like quadratic equations or systems of equations. These will introduce you to more complex techniques, such as factoring, using the quadratic formula, or using substitution and elimination methods. Each type of equation will challenge you in unique ways, strengthening your problem-solving abilities.
Word Problems: Apply your equation-solving skills to word problems. Word problems are great because they force you to translate real-world scenarios into mathematical equations. This is one of the most practical applications of algebra, as you'll often encounter similar situations in everyday life, from budgeting to calculating distances.
Inequalities: Try solving inequalities. Inequalities are similar to equations but involve comparison symbols like <, >, ≤, and ≥. This will help you understand the concept of ranges and how variables can have multiple possible values. This will give you another level of analysis.
Practice, Practice, Practice: The more you practice, the better you’ll get! Work through a variety of problems to build your confidence and become more comfortable with the different steps involved.

Conclusion: Mastering the Equation Game

So, there you have it, folks! We've successfully navigated the equation, found the value of m, and calculated the final expression. Remember that the key to mastering these types of problems is understanding the underlying principles and practicing consistently. By breaking down the problem step-by-step, we were able to solve it efficiently and accurately. Keep practicing, keep exploring, and you'll be well on your way to becoming a math whiz. The ability to solve equations is a crucial skill in many areas of life, from science and engineering to finance and everyday problem-solving. Keep up the awesome work!

This journey has hopefully boosted your confidence and given you the tools to tackle similar problems with ease. Now, go forth and conquer those equations! Remember, math is like any other skill – the more you practice, the better you become. Don't be afraid to make mistakes; they're an essential part of the learning process. Celebrate your successes, and keep striving to improve. Good luck, and keep those math muscles flexed!