Solve For X: Equation $\frac{4 X+27}{3}=5$

Hey guys, welcome back to Plastik Magazine! Today, we're diving deep into the world of mathematics, tackling a classic algebra problem: solving for $x$. It might sound intimidating, but trust me, by breaking it down step-by-step, even the most complex equations can become surprisingly manageable. Our specific equation for today is $\frac{4 x+27}{3}=5$. Now, before we jump into the nitty-gritty, let's talk about why understanding how to solve for a variable like $x$ is so darn important. Think of $x$ as a mystery box. Our goal is to figure out what's inside that box, what number or value makes the entire equation true. This skill isn't just for math class; it's a fundamental building block for problem-solving in countless real-world scenarios, from managing your budget to understanding scientific data. So, let's get ready to unlock that mystery box and find the value of $x$!

Understanding the Equation

Alright, let's really dissect this equation: $\frac{4 x+27}{3}=5$. What we have here is a linear equation. The term 'linear' basically means that if you were to graph this equation, you'd get a straight line. No curves, no funky shapes, just a nice, clean line. Our main objective, as we mentioned, is to isolate $x$ on one side of the equation. To do this, we need to peel away all the numbers and operations that are currently attached to $x$. Think of it like unwrapping a present – you have to carefully remove each layer to get to the prize inside. In our equation, $x$ is being multiplied by 4, then 27 is being added to that result, and finally, the entire sum is being divided by 3. Our mission is to reverse these operations in the correct order. Remember the order of operations (PEMDAS/BODMAS)? When we're solving equations, we often have to undo operations in the reverse order. So, instead of Parentheses, Exponents, Multiplication/Division, Addition/Subtraction, we'll be thinking about undoing Addition/Subtraction first, then Multiplication/Division, and so on. This systematic approach is key to successfully solving for $x$ without getting lost. So, let's get our mathematical detective hats on and prepare to systematically unravel this equation. We're not just finding a number; we're mastering a crucial problem-solving technique that will serve you well beyond the realm of algebra.

Step 1: Isolate the Numerator

The first big hurdle we need to overcome is that division by 3. The entire expression $(4x + 27)$ is currently trapped under that division bar. To free it, we need to perform the inverse operation of division, which is multiplication. We're going to multiply both sides of the equation by 3. Why both sides, you ask? Because an equation is like a perfectly balanced scale. Whatever you do to one side, you must do to the other to keep it balanced. If we only multiplied the left side by 3, the equation would be thrown off, and our solution would be incorrect. So, let's do it:

$\frac{4 x+27}{3} \times 3 = 5 \times 3$

On the left side, the multiplication by 3 and the division by 3 cancel each other out, leaving us with just the numerator:

$4x + 27$

And on the right side, $5 \times 3$ gives us:

$15$

So, our equation has now been simplified to:

$4x + 27 = 15$

See? We've already made significant progress! That fraction is gone, and $x$ is looking a little less crowded. This is a crucial step in isolating $x$, and it's all about applying inverse operations to maintain the equality of the equation. Remember, guys, every step we take is deliberate and serves a purpose in simplifying the problem. We're systematically dismantling the equation piece by piece to get to that elusive value of $x$. Keep that focus, and you'll conquer this!

Step 2: Isolate the Term with x

Now that we've got $4x + 27 = 15$, our next target is to get the term that contains $x$ – which is $4x$ – all by itself. Currently, 27 is hanging out with $4x$, being added to it. To get rid of that '+ 27', we need to perform the inverse operation, which is subtraction. Just like before, we must subtract 27 from both sides of the equation to maintain the balance. This is super important, folks. If we only subtract it from one side, our equation becomes unbalanced, and our $x$ will be off.

So, let's subtract 27 from both sides:

$4x + 27 - 27 = 15 - 27$

On the left side, the $+ 27$ and $- 27$ cancel each other out, leaving us with just $4x$:

$4x$

On the right side, we perform the subtraction: $15 - 27$. This gives us:

$-12$

Our equation is now looking even simpler:

$4x = -12$

Boom! We're so close now. The $4x$ term is isolated. We've successfully removed the constant term (27) that was interfering with our goal of isolating $x$. This step highlights the power of inverse operations in algebra. By consistently applying the opposite action to both sides, we systematically simplify the equation, moving closer and closer to revealing the value of $x$. Each subtraction, each multiplication, is a calculated move in our quest to solve this puzzle. Keep pushing, we're almost there!

Step 3: Solve for x

We've reached the final frontier, guys! Our equation is now $4x = -12$. This means