Solve For M: (1/2)m - (3/4)n = 16, N=8

Hey guys! Ever stumbled upon an equation that looks a bit intimidating but is actually quite simple to solve? Today, we're diving into one such equation where we need to find the value of 'm'. Specifically, we're tackling the equation: (1/2)m - (3/4)n = 16, and we already know that n = 8. Sounds like a puzzle, right? Let's break it down together, step by step, and see how easy it is to find the value of 'm'. Think of it as a fun little mathematical adventure! We'll use basic algebraic principles, and by the end of this guide, you'll be a pro at solving similar equations. So, grab your imaginary pencils, and let's get started on this mathematical journey to uncover the mystery of 'm'. This isn't just about getting the right answer; it's about understanding the process and building your problem-solving skills. Remember, mathematics is like a language, and once you learn the grammar (the rules), you can express all sorts of ideas. So, let's learn some mathematical grammar today and add another tool to your problem-solving toolkit.

Step 1: Substitute the Value of n

The first move in our mathematical game is to use the information we already have. We know that n = 8, so let's plug that value into our equation. This is like replacing a piece in a jigsaw puzzle – we're fitting the known value into the right spot. Our equation, (1/2)m - (3/4)n = 16, now transforms into (1/2)m - (3/4)(8) = 16. See how we've simply swapped 'n' with '8'? This might seem like a small step, but it's a crucial one. By substituting the known value, we've reduced the number of unknowns in our equation, making it simpler to solve. Think of it as narrowing down the possibilities – we're one step closer to finding 'm'. Now that we've made this substitution, the next step involves simplifying the equation further. We'll deal with the multiplication in the next step, making sure we follow the order of operations. Remember, in mathematics, just like in life, following the correct order is key to success. So, we've laid the groundwork; let's move on to the next stage of our mathematical quest and continue simplifying our equation.

Step 2: Simplify the Equation

Now that we've substituted the value of 'n', it's time to tidy things up a bit. Our equation currently looks like this: (1/2)m - (3/4)(8) = 16. The next logical step is to perform the multiplication: (3/4) multiplied by 8. If you think of 8 as 8/1, this multiplication becomes straightforward: (3/4) * (8/1) = 24/4. And what is 24 divided by 4? It's 6! So, we've simplified (3/4)(8) to 6. Our equation now looks even cleaner: (1/2)m - 6 = 16. We're making good progress, guys! We've reduced the complexity of the equation by performing the multiplication. This is a classic technique in algebra – simplify as much as you can before moving on to the next step. It's like clearing away the clutter on your desk before starting a project; it makes everything easier to manage. By simplifying the equation, we're making it more manageable and bringing ourselves closer to isolating 'm'. So, let's keep up this momentum and move on to the next step in our journey to find the value of 'm'.

Step 3: Isolate the Term with 'm'

We're on a roll! Our equation is now in a much friendlier form: (1/2)m - 6 = 16. Our mission in this step is to get the term with 'm' – which is (1/2)m – all by itself on one side of the equation. To do this, we need to get rid of the - 6 that's hanging out on the same side. How do we do that? We use the magic of inverse operations! Since we're subtracting 6, the inverse operation is adding 6. So, we'll add 6 to both sides of the equation. Remember, what we do to one side of the equation, we must do to the other to keep things balanced. This is a fundamental principle in algebra – maintaining equality. Adding 6 to both sides gives us: (1/2)m - 6 + 6 = 16 + 6. The - 6 and + 6 on the left side cancel each other out, leaving us with just (1/2)m. On the right side, 16 + 6 equals 22. So, our equation now beautifully simplifies to: (1/2)m = 22. We've successfully isolated the term with 'm'! This is a major milestone in solving for 'm'. We're almost there, guys! Just one more step to go, and we'll have our answer. Let's keep up the great work and move on to the final stage of our mathematical adventure.

Step 4: Solve for 'm'

Alright, we've reached the final stretch! Our equation is looking sleek and simple: (1/2)m = 22. We're so close to uncovering the value of 'm'! Right now, 'm' is being multiplied by 1/2. To isolate 'm' completely, we need to undo this multiplication. What's the inverse operation of multiplying by 1/2? It's multiplying by the reciprocal of 1/2, which is 2. So, we're going to multiply both sides of our equation by 2. Again, we need to keep that balance – what we do to one side, we must do to the other. Multiplying both sides by 2 gives us: 2 * (1/2)m = 2 * 22. On the left side, 2 multiplied by 1/2 cancels out, leaving us with just 'm'. On the right side, 2 multiplied by 22 equals 44. And there you have it! Our equation now proudly proclaims: m = 44. We've done it, guys! We've successfully solved for 'm'. It might have seemed like a daunting task at first, but by breaking it down into manageable steps, we conquered it. This is the power of algebra – taking complex problems and solving them piece by piece. So, let's celebrate our mathematical victory and take a moment to reflect on what we've learned.

Conclusion:

Awesome job, everyone! We successfully navigated the equation (1/2)m - (3/4)n = 16 with n = 8 and discovered that m = 44. Wasn't that a fun journey? We started with a seemingly complex equation, but by methodically substituting values, simplifying, isolating terms, and using inverse operations, we arrived at our solution. This process is the heart of algebra, and it's a skill that will serve you well in all sorts of mathematical adventures. Remember, guys, mathematics isn't just about numbers and symbols; it's about problem-solving, logical thinking, and perseverance. Each equation is like a puzzle waiting to be solved, and with the right tools and techniques, you can crack any mathematical code. So, keep practicing, keep exploring, and keep that mathematical curiosity alive! The world of mathematics is vast and fascinating, and there's always something new to learn. And who knows? Maybe the next mathematical puzzle you solve will be even more exciting than this one. So, until next time, happy solving!