Solve Math: Number Multiplied By 6 Plus 12 Equals 48

Hey guys! Ever get those math problems that look like a jumbled mess of numbers and operations? Let's break one down today and see how easy it can be to solve. We're going to tackle a problem that involves multiplication and addition, and I promise, it's not as scary as it sounds. Think of it like a puzzle – we just need to find the missing piece!

Understanding the Problem

The problem we're looking at is this: If you multiply a number by 6 and add 12, you get 48. What's the number?. Sounds like a riddle, right? But it's just a straightforward math equation in disguise. The key to cracking these problems is translating the words into mathematical symbols. Let's dissect it piece by piece. The first part says, “If you multiply a number by 6…” We don't know the number yet, so let's call it "x". Multiplying it by 6 gives us 6x. Next, it says, “…and add 12…” So, we take our 6x and add 12 to it, making it 6x + 12. The final part tells us, “…you get 48.” This means our entire expression, 6x + 12, is equal to 48. Now we have our equation: 6x + 12 = 48. See? We've turned a wordy problem into a neat little equation. This is the crucial first step in solving any math problem – understanding what it's really asking and putting it into a form we can work with. It's like translating from one language to another, but in this case, we're going from English to Math! Remember, every word in the problem is a clue. Don't skim over anything. Read it carefully and think about what each part means mathematically. Once you've got that equation, you're halfway to the solution.

Setting Up the Equation

Now that we've got a handle on the problem, let's dive deeper into setting up the equation. I know equations might seem intimidating, but they're just a way of showing relationships between numbers. In our case, the relationship is between our unknown number, the operations we perform on it, and the final result. So, as we discussed, the phrase "a number multiplied by 6" translates to 6 * x, or simply 6x. The variable x is our mystery number, the one we're trying to find. This is a common trick in algebra – using letters to stand in for values we don't know yet. It's like giving a name to the unknown, which makes it easier to talk about and manipulate. Then, we have the addition of 12, which we write as + 12. And finally, the phrase "obtains 48" tells us that the whole expression equals 48, so we write = 48. Putting it all together, we get the equation 6x + 12 = 48. This equation is the heart of our problem. It's a mathematical sentence that tells us exactly what's going on. The left side, 6x + 12, represents the operations we're performing on our unknown number. The right side, 48, is the result we get. Our goal now is to isolate x, to get it all by itself on one side of the equation. This will tell us the value of our mystery number. Think of the equals sign (=) as a balance scale. Whatever we do to one side of the equation, we have to do to the other side to keep the scale balanced. This is a fundamental principle in algebra, and it's what allows us to solve for x. So, with our equation set up, we're ready for the next step: solving it.

Solving the Equation Step-by-Step

Alright, guys, we've got our equation: 6x + 12 = 48. Now for the fun part – solving it! Remember, our goal is to get 'x' all by itself on one side of the equation. To do this, we're going to use something called inverse operations. Think of them as the opposite of the operations in the equation. If we see addition, we'll use subtraction. If we see multiplication, we'll use division, and so on. The first thing we want to get rid of is the + 12. The inverse operation of addition is subtraction, so we're going to subtract 12 from both sides of the equation. This keeps our balance scale even. So, we have: 6x + 12 - 12 = 48 - 12. On the left side, the +12 and -12 cancel each other out, leaving us with just 6x. On the right side, 48 - 12 equals 36. Now our equation looks like this: 6x = 36. We're getting closer! Next, we need to get rid of the 6 that's multiplying our 'x'. The inverse operation of multiplication is division, so we're going to divide both sides of the equation by 6. This gives us: 6x / 6 = 36 / 6. On the left side, the 6s cancel each other out, leaving us with just 'x'. On the right side, 36 divided by 6 equals 6. And there you have it! Our equation is now: x = 6. We've solved for 'x'! This means that the number we were looking for is 6. Solving equations might seem like a complex process, but it's really just a matter of following these steps: identify the operations, use inverse operations to isolate the variable, and keep the equation balanced. With a little practice, you'll be solving equations like a pro!

Checking Your Answer

Okay, we've found our answer: x = 6. But how do we know we're right? This is where checking our answer comes in. It's a super important step in any math problem. It's like proofreading your work in English class – it helps you catch any mistakes you might have made. To check our answer, we're going to take the value we found for 'x' (which is 6) and plug it back into our original equation: 6x + 12 = 48. So, we replace 'x' with 6, giving us: 6 * 6 + 12 = 48. Now we just need to simplify the left side of the equation to see if it equals 48. First, we do the multiplication: 6 * 6 = 36. So, our equation becomes: 36 + 12 = 48. Next, we do the addition: 36 + 12 = 48. And look at that! We get 48 = 48. This means our answer is correct! The left side of the equation equals the right side, so we know we've found the right value for 'x'. Checking your answer is like having a secret weapon. It gives you confidence that you've solved the problem correctly, and it helps you learn from any mistakes you might have made. If the left side of the equation doesn't equal the right side, it means you need to go back and check your work. Maybe you made a mistake in your calculations, or maybe you set up the equation incorrectly. Either way, checking your answer is a great way to catch those errors and improve your math skills. So, always remember to check your work – it's worth the extra effort!

The Answer and its Significance

So, after all that work, what's the final answer? Drumroll, please… The number is 6! We figured it out by translating the word problem into an equation, solving the equation step-by-step, and then checking our answer to make sure we were right. But beyond just getting the right answer, it's important to think about what this means. We've not only found a number that fits a specific set of conditions, but we've also used some powerful mathematical tools along the way. We've practiced translating words into mathematical symbols, setting up and solving equations, and using inverse operations. These are skills that will come in handy in all sorts of situations, both in and out of the classroom. Think about it: equations are used to model everything from the trajectory of a rocket to the growth of a population. Understanding how to solve them opens up a whole world of possibilities. And the process we used to solve this problem – breaking it down into smaller steps, using logical reasoning, and checking our work – is a valuable approach to problem-solving in general. Whether you're tackling a tough math problem or trying to figure out a real-life challenge, these skills will help you succeed. So, the next time you see a math problem that looks intimidating, remember this example. Break it down, set up an equation, solve it step-by-step, and don't forget to check your answer. You've got this! And remember, math isn't just about numbers; it's about thinking, reasoning, and problem-solving. Keep practicing, keep exploring, and you'll be amazed at what you can accomplish.