Solving For X: A Simple Equation Explained

Hey guys! Ever get stuck trying to solve for x in an equation? It can feel like you're trying to decipher a secret code, right? Well, don't sweat it! We're going to break down a super common type of problem where you need to isolate x and figure out its value. Let's take the equation 70 = (14x)/3 as our example. This might seem a bit daunting at first, but trust me, with a few simple steps, you'll be solving these like a pro in no time. The key is to understand the order of operations and how to reverse them to get x all by itself on one side of the equation. So, grab your pencil and paper (or your favorite notes app!), and let's dive in. We'll go through each step slowly and explain why we're doing what we're doing. By the end of this guide, you'll not only be able to solve this specific equation but also have a solid understanding of how to tackle similar problems in the future. Remember, math is like building blocks; once you understand the basics, you can build on that knowledge to solve more complex problems. So, let's get started and unlock the mystery of solving for x!

Understanding the Equation: 70 = (14x)/3

Okay, so before we jump into solving, let's make sure we really understand what this equation, 70 = (14x)/3, is telling us. Think of an equation like a balanced scale. The equals sign (=) means that whatever is on the left side has the same value as whatever is on the right side. In this case, the number 70 is perfectly balanced with the expression (14x)/3. Our mission is to figure out what value of x will keep that scale balanced. The left side is straightforward: it's just the number 70. The right side is a little more interesting. It says, "Take some number x, multiply it by 14, and then divide the result by 3." The result of all that must equal 70 for the equation to be true. Another way to think about it is that 14x represents fourteen times an unknown value. When you divide that result by 3, you get 70. So, a number multiplied by 14, then divided by 3 equals 70. Breaking it down like this helps to visualize the relationship between the numbers and the unknown variable. We need to reverse the operations to isolate x. We need to undo the division by 3 and the multiplication by 14. Once we have x by itself on one side of the equals sign, we'll know its value. Understanding this fundamental concept is crucial for solving any algebraic equation. It's not just about following steps blindly; it's about grasping the underlying relationships between the numbers and variables. So, with this understanding in mind, let's move on to the first step in solving for x.

Step 1: Multiplying Both Sides by 3

The first thing we want to do is get rid of that fraction. To do this, we'll multiply both sides of the equation by 3. Remember, whatever we do to one side of the equation, we must do to the other side to keep it balanced! So, we start with: 70 = (14x)/3. Now, we multiply both sides by 3: 3 * 70 = 3 * (14x)/3. On the left side, 3 * 70 equals 210. On the right side, the 3 in the numerator and the 3 in the denominator cancel each other out. This is because multiplying by 3 and then dividing by 3 is the same as doing nothing. So, we are left with: 210 = 14x. See how much simpler that looks? By multiplying both sides by 3, we've eliminated the fraction and brought us one step closer to isolating x. The equation now tells us that 14 times x equals 210. Our next step will be to undo the multiplication by 14. But before we move on, let's quickly recap why we multiplied by 3. We did this to eliminate the division by 3 on the right side of the equation. By performing the opposite operation (multiplication), we simplified the equation and made it easier to solve for x. This is a common strategy in algebra: use inverse operations to isolate the variable you're trying to solve for. So, with this step completed, we're well on our way to finding the value of x. Let's move on to the next step!

Step 2: Dividing Both Sides by 14

Alright, now we're at the point where our equation looks like this: 210 = 14x. Our goal is to get x all by itself on one side of the equation. Right now, x is being multiplied by 14. To undo this multiplication, we need to do the opposite operation: division. So, we're going to divide both sides of the equation by 14. This gives us: 210 / 14 = (14x) / 14. On the left side, 210 divided by 14 equals 15. On the right side, the 14 in the numerator and the 14 in the denominator cancel each other out, leaving us with just x. So, our equation simplifies to: 15 = x. And there you have it! We've successfully isolated x and found its value. This step was all about using the inverse operation of multiplication (which is division) to get x by itself. By dividing both sides of the equation by 14, we effectively "undid" the multiplication and revealed the value of x. It's important to remember that whatever you do to one side of the equation, you must do to the other side to maintain the balance. In this case, dividing both sides by 14 ensured that the equation remained true and that we arrived at the correct value for x. So, with this step completed, we can confidently say that we've solved for x. But before we declare victory, let's do one final check to make sure our answer is correct.

Step 3: Checking Your Answer

Okay, so we've found that x = 15. But how do we know if we're right? The best way to be sure is to plug our answer back into the original equation and see if it holds true. Our original equation was: 70 = (14x)/3. Now, let's substitute 15 for x: 70 = (14 * 15) / 3. First, we need to calculate 14 * 15. If you do the math (or use a calculator), you'll find that 14 * 15 = 210. So, now our equation looks like this: 70 = 210 / 3. Next, we need to divide 210 by 3. And guess what? 210 / 3 = 70. So, our equation becomes: 70 = 70. And that's true! The left side of the equation equals the right side of the equation. This means that our answer, x = 15, is correct. By plugging our answer back into the original equation, we've verified that it satisfies the equation and keeps the balance. This step is super important because it helps you catch any mistakes you might have made along the way. It's always a good idea to check your work, especially in math. So, with this final check, we can confidently say that we've successfully solved for x and that our answer is correct. Give yourself a pat on the back! You've conquered another algebraic equation. Let's summarize the steps.

Summary: Steps to Solve for x

Alright, let's recap the steps we took to solve for x in the equation 70 = (14x)/3:

1. Multiply both sides by 3: This eliminated the fraction and gave us the equation 210 = 14x.
2. Divide both sides by 14: This isolated x and gave us the solution x = 15.
3. Check your answer: Plug x = 15 back into the original equation to verify that it holds true.

By following these steps, you can solve similar equations where you need to isolate x. Remember the key principles:

• Keep the equation balanced: Whatever you do to one side, do to the other.
• Use inverse operations: To undo an operation, use its opposite (e.g., multiplication and division).
• Check your work: Always plug your answer back into the original equation to verify that it's correct.

With these principles in mind, you'll be well-equipped to tackle a wide range of algebraic equations. Keep practicing, and you'll become a master at solving for x! It just takes time, patience, and a willingness to learn from your mistakes. So, don't be afraid to make mistakes; they're part of the learning process. Just keep practicing, and you'll eventually get there. You've got this! Remember, solving for x is a fundamental skill in algebra, and it's a skill that will serve you well in many areas of math and science. So, keep honing your skills, and you'll be amazed at what you can accomplish.

Now, go forth and solve some equations! You've earned it!