How to Solve the Equation 6x - 48 = 6 for x

Cracking the Code: Solving Linear Equations Like a Pro

Let’s be real for a second—equations can feel like a foreign language sometimes. You’ve got letters, numbers, and symbols all dancing together on that paper, and it’s easy to feel like you’re left out of the party. But solving linear equations, like the one we’ll tackle today, can be simpler than you think! Let’s break it down together and find that “aha” moment.

What’s the Equation?

Take a look at this equation:

6x - 48 = 6

At first glance, it might look intimidating, but trust me, it’s not as scary as it seems. It’s a linear equation, which typically means that when we’re done, we’re gonna find out the value of x. Now, wouldn’t that be a satisfying ending?

The Goal: Isolate That Variable!

When we solve an equation, our main objective is to isolate x—basically, we want x to be standing proudly on one side of the equation, all alone, with a value that makes sense. So, how do we get there?

Step 1: Add 48 Like a Boss

First things first, let’s get rid of what’s dragging x down. In our equation, that’s the -48. To do this, we’ll add 48 to both sides. Remember, whatever you do to one side, you must do to the other to keep everything balanced. It’s like walking a tightrope; one wrong move and you could fall!

So, let’s do the math:

6x - 48 + 48 = 6 + 48

This simplifies to:

6x = 54

You feel that? That’s the weight lifted off our equation!

Step 2: Divide and Conquer

Next up, we need to get x by itself. To do that, we need to divide both sides by the number that’s currently shackling x—yep, that’s the 6 hanging out with it.

So, here we go:

6x / 6 = 54 / 6

This leads us to:

x = 9

And there we have it! The solution is x = 9. But hang on a second—let's make sure that fits into our original equation like a puzzle piece.

Plugging the Answer Back In

Let’s play detective for a moment. What if we throw our found value back into the original equation to see if everything checks out? Trust me, it’s a must!

So we have:

6(9) - 48 = 6

If we calculate that, we get:

54 - 48 = 6

And lo and behold, it actually equals 6! Our answer fits snugly like a glove. But wait, what about the other options? Let’s break them down too, just for kicks.

What About the Other Choices?

• A. -6

• If we plug -6 into the equation:

• 6(-6) - 48 = -36 - 48 = -84. Not equal to 6.

• B. 6

• Here’s the math:

• 6(6) - 48 = 36 - 48 = -12. Nope, still not 6.

• C. 9

• Oh wait, we already solved this one!

• D. 12

• Let’s check it out:

• 6(12) - 48 = 72 - 48 = 24. Nope, not equal to 6 either.

Looks like we found our champion: x = 9.

A Quick Recap

So, there you have it! Isolating x from the original equation led us to the answer, showing us that math doesn’t have to budge when you know the steps. It’s kind of like conquering a video game level—once you know the strategy, the challenges become opportunities.

Equations bring logic and problem-solving into our everyday lives. From budgeting your allowance to calculating how much time you have left for that Netflix binge, knowing how to solve equations simplifies things like a trusty GPS in an unfamiliar city.

Why This Matters

Learning to tackle equations, even ones that seem tricky at first, perfectly prepares you for the more complex challenges around us—whether that’s in learning another subject, thinking through a project at work, or solving real-world problems. And yes, math is everywhere, waiting to be unraveled.

Are you feeling inspired yet? Or maybe you’ve seen just how smoothing these math roads can be? Keep practicing, keep learning. There’s a whole world out there where being confident in your math skills can open doors—kind of like having a secret superpower.

So, grab your pencil, put on your thinking cap, and let’s keep this mathematical journey going strong! You know what? The more you practice, the better you'll get. And who knows—maybe soon you'll be the one solving equations faster than your friends can say, “What’s for lunch?”

Happy solving!