Hey guys! Today, we're diving into a fun little math problem that involves finding the value of x in a linear equation. Equations might seem intimidating at first, but trust me, they're just puzzles waiting to be solved. We're given the equation 3x - 4y = 55, and we know that y = 4. Our mission? To figure out what x is. So, let's get started and break this down step by step!
Plugging in the Value of Y
The first crucial step in solving this equation is to substitute the given value of y into the equation. We know that y = 4, so we'll replace every instance of y in the equation with 4. This gives us a new equation that looks like this: 3x - 4(4) = 55. Now, we've got a simpler equation with only one variable, x, which makes our job much easier. This substitution is a fundamental technique in algebra, allowing us to reduce complex equations into more manageable forms. Remember, the key is to isolate the variable we're trying to find, and substitution is our first move in that direction. Think of it like replacing a piece in a jigsaw puzzle – we're fitting the known value of y into the larger picture to reveal the unknown value of x. The beauty of algebra lies in this ability to manipulate equations, using known quantities to uncover hidden ones. It's like detective work, where each step brings us closer to the solution. So, with y now out of the way, let's move on to the next stage of our mathematical quest and see what else we can simplify.
Simplifying the Equation
Alright, now that we've plugged in the value of y, it's time to simplify the equation. We have 3x - 4(4) = 55. The first thing we need to do is take care of the multiplication: 4 multiplied by 4. That's a straightforward calculation, and it gives us 16. So, our equation now looks like this: 3x - 16 = 55. See how much cleaner that looks already? Simplifying equations is all about making them easier to work with, and getting rid of those parentheses is a big step in the right direction. Think of it like decluttering a room – once you remove the unnecessary stuff, you can see the important things more clearly. In this case, the "unnecessary stuff" was the multiplication, and now we can focus on isolating x. Remember, the goal is to get x by itself on one side of the equation, and we're making progress one step at a time. Each simplification is a victory, bringing us closer to the final answer. So, with the multiplication out of the way, let's move on to the next step and continue our journey towards solving for x.
Isolating the Term with X
Okay, guys, let's keep this momentum going! We're at the stage where we need to isolate the term with x. Our equation currently reads 3x - 16 = 55. To get the 3x term by itself, we need to get rid of that -16. How do we do that? Simple! We perform the opposite operation. Since we're subtracting 16, we'll add 16 to both sides of the equation. This is a crucial step because it maintains the balance of the equation. Think of it like a seesaw – whatever you do to one side, you have to do to the other to keep it level. So, adding 16 to both sides gives us: 3x - 16 + 16 = 55 + 16. On the left side, the -16 and +16 cancel each other out, leaving us with just 3x. On the right side, 55 + 16 equals 71. So, our equation is now 3x = 71. We're getting so close! We've successfully isolated the term with x, and now we just have one more step to take to find the value of x itself. Let's head to the final stretch and conquer this equation!
Solving for X
Alright, we're in the home stretch now! Our equation is 3x = 71. Remember, our ultimate goal is to find the value of x. Right now, x is being multiplied by 3. To isolate x completely, we need to perform the opposite operation: division. We'll divide both sides of the equation by 3. This keeps the equation balanced, just like adding 16 to both sides did in the previous step. So, we have 3x / 3 = 71 / 3. On the left side, the 3 in the numerator and the 3 in the denominator cancel each other out, leaving us with just x. On the right side, 71 / 3 is a division problem. When we perform this division, we get 23 with a remainder of 2. This means that 71 / 3 is equal to the mixed number 23 2/3. So, we've finally found it! The value of x is 23 2/3. That's it! We've successfully navigated the equation and emerged victorious. Pat yourselves on the back, guys – you've earned it! Now, let's recap our journey and see how we arrived at this answer.
Recap of the Solution
Let's take a moment to recap the steps we took to solve this equation. We started with 3x - 4y = 55 and y = 4. First, we plugged in the value of y, which gave us 3x - 4(4) = 55. Then, we simplified the equation by performing the multiplication, resulting in 3x - 16 = 55. Next, we isolated the term with x by adding 16 to both sides, which gave us 3x = 71. Finally, we solved for x by dividing both sides by 3, which led us to the answer: x = 23 2/3. See? When we break it down step by step, even complex-looking equations become manageable. It's all about following the rules of algebra and taking your time. Each step builds upon the previous one, bringing you closer to the solution. And remember, practice makes perfect! The more equations you solve, the more comfortable you'll become with the process. So, don't be afraid to tackle those mathematical puzzles – you've got this! Now that we've recapped the solution, let's take a look at the answer choices provided and see which one matches our result.
Matching the Answer Choice
Now that we've confidently solved for x and found that x = 23 2/3, let's compare our answer to the options provided. We have four choices:
A. x = 13 1/4 B. x = 21 2/3 C. x = 23 D. x = 27
Looking at these options, it's clear that option B, x = 21 2/3, matches our calculated value of x. This confirms that our step-by-step solution was accurate, and we've successfully navigated this mathematical puzzle. It's always a satisfying feeling when your hard work pays off and you arrive at the correct answer! This process of matching your solution to the provided options is a crucial step in problem-solving. It allows you to double-check your work and ensure that you haven't made any errors along the way. So, always take the time to compare your answer to the choices given – it's a valuable habit that will help you succeed in mathematics and beyond. With our answer confirmed, we can confidently move on to the next challenge, knowing that we've mastered this particular type of equation. Keep up the great work, guys!
So, there you have it, guys! We've successfully solved for x in the equation 3x - 4y = 55, when y = 4. We followed a systematic approach, substituting the value of y, simplifying the equation, isolating the term with x, and finally, solving for x. Our journey led us to the answer: x = 23 2/3. Remember, math problems are like puzzles, and each step is a piece that fits into the bigger picture. By breaking down complex equations into smaller, manageable steps, we can conquer any mathematical challenge. The key is to understand the underlying principles, practice regularly, and never be afraid to ask for help when you need it. You've all done an amazing job following along, and I'm confident that you'll be able to tackle similar problems with ease. Keep practicing, keep learning, and most importantly, keep having fun with math! You've got this!