Unlock X: Simple Steps To Solve (115-x)*2=36 Easily
Welcome to the World of Linear Equations!
Hey there, math explorers! Ever looked at an equation like (115-x)*2=36 and felt a tiny bit overwhelmed? Or maybe a huge bit overwhelmed? Don't sweat it, because you're in the perfect place to conquer it! Today, we're diving deep into the fascinating world of linear equations, specifically tackling this very problem, and I promise you, by the end of this article, you'll not only know how to solve it but also why each step makes perfect sense. Think of this as your friendly guide to becoming a bona fide equation-solving superstar. Math isn't just about numbers and formulas; it's about problem-solving, critical thinking, and unlocking the mysteries of the universe, one x at a time. And guess what? Linear equations are the bedrock of so much of that understanding. They're everywhere, from figuring out your budget for the month to calculating how much paint you need for a room, or even in the complex algorithms that power your favorite apps. They might seem abstract at first glance, but these simple algebraic expressions are incredibly powerful tools that help us model and understand the world around us. So, if you've ever wondered how to approach such a problem, or if you're just looking to solidify your algebra skills, grab a comfy seat, maybe a snack, and let's embark on this awesome learning journey together. We're not just finding a single number here; we're building a foundational understanding that will serve you well in countless situations, both inside and outside the classroom. Mastering these basic concepts is like learning the ABCs of mathematics – once you get them down, a whole new language of understanding opens up to you. So, ready to find X and unveil the hidden value in our equation? Let's do this, buddies! We'll break down every single step, making sure no one gets left behind. This isn't just about memorizing a sequence of actions; it's about genuinely comprehending the logic and reasoning behind each move we make. And trust me, once you grasp that, you'll feel an incredible sense of accomplishment. Understanding these fundamental building blocks is key to tackling more complex mathematical challenges down the road. Let's make math fun and accessible, showing everyone that they too can master these powerful problem-solving techniques. You've got this!
Cracking the Code: Solving (115-x)*2=36 Together
Alright, guys, let's get down to business and solve our target equation: (115-x)*2=36. This isn't just about getting the right answer; it's about understanding the journey to that answer. We're going to break it down step-by-step, explaining the logic behind each move, so you can apply these principles to any similar problem you encounter. Think of it as peeling back the layers of an onion, but way less tear-inducing! Our ultimate goal in solving any linear equation is to isolate the variable, which in this case is x. We want to get x all by itself on one side of the equals sign. To do this, we'll use a series of inverse operations – essentially, undoing whatever has been done to x. Remember, whatever you do to one side of the equation, you must do to the other side to keep it balanced, like a perfectly level seesaw. That's the golden rule of algebra! So, let's start with our equation: (115-x)*2=36.
Step 1: Undo the Multiplication
Our first order of business is to tackle that *2 on the left side. The entire expression (115-x) is being multiplied by 2. To undo multiplication, we use its inverse operation: division. So, we're going to divide both sides of the equation by 2. This is crucial for beginning to chip away at the layers surrounding x. If we only divided one side, our seesaw would tip, and the equation would no longer be true. So, (115-x)*2 / 2 = 36 / 2. On the left, the *2 and /2 cancel each other out, leaving us with 115-x. On the right, 36 / 2 simplifies to 18. Now our equation looks much simpler: 115-x = 18. See? We're already making great progress! This step is often where folks might try to distribute the 2 first (2115 - 2x = 36). While that's mathematically correct, it often adds an extra step and can sometimes lead to more opportunities for small errors, especially with negative signs. Dividing first is usually the cleaner path when the entire side is multiplied by a single number.
Step 2: Isolate the Term with X
Now we have 115-x = 18. Our variable x is still attached to the 115 by subtraction. To isolate -x, we need to get rid of that 115. Since 115 is a positive number being added (or rather, -x is being subtracted from 115), its inverse operation is subtraction. So, we will subtract 115 from both sides of the equation. This moves the constant term away from our variable. On the left side, 115 - 115 - x simply becomes -x (because 115 - 115 is zero, leaving just the -x). On the right side, we have 18 - 115. This calculation results in a negative number: 18 - 115 = -97. So, our equation now reads: -x = -97. You're doing awesome!
Step 3: Solve for Positive X
We're almost there! We currently have -x = -97. But we don't want to know what negative x is; we want to know what positive x is. Think of -x as (-1)*x. To get x by itself, we need to divide both sides by -1 (or multiply by -1, it achieves the same result). So, if we divide both sides by -1, we get (-x) / -1 = (-97) / -1. A negative divided by a negative equals a positive, so -x / -1 becomes x, and -97 / -1 becomes 97. Voila! We've found our x! x = 97.
Checking Your Answer (Always a Good Idea!)
Before you high-five yourself (which you totally should!), it's a fantastic habit to check your answer. Plug x=97 back into the original equation: (115-x)*2=36.
- Substitute
xwith97:(115 - 97) * 2 = 36 - First, perform the operation inside the parentheses:
115 - 97 = 18 - Now the equation is:
(18) * 2 = 36 - And finally:
36 = 36.
Since both sides match, our solution x=97 is absolutely correct! See, guys? It's not magic; it's just following the rules of algebra consistently. You just cracked the code!
Unpacking the Power of Algebra: Core Principles You Need to Know
Alright, now that we've successfully navigated the specific problem (115-x)*2=36, let's zoom out a bit and talk about the why behind the how. Understanding these core principles of algebra isn't just about solving a single equation; it's about building a robust mental toolkit that empowers you to tackle any linear equation that comes your way. Think of these as the fundamental rules of the game. First up, let's clarify what a variable is. In our equation, x is the variable. A variable is essentially a placeholder, usually a letter (like x, y, a, b, etc.), that represents an unknown value. Our entire quest when solving an equation is to discover what specific number that variable stands for. It's like a mystery character in a story, and we're the detectives trying to uncover their identity. The beauty of variables is that they allow us to generalize problems and describe relationships between different quantities without knowing their exact numerical values upfront. This abstraction is incredibly powerful and forms the backbone of mathematical modeling. Without variables, algebra as we know it simply wouldn't exist, making complex problem-solving much, much harder.
Next, let's talk about inverse operations. This concept is absolutely crucial. Every mathematical operation has an