How to Solve the Equation 2(x - 3) = 8: A Clear Guide

Understanding the Equation: 2(x - 3) = 8

Equations can sometimes feel like riddles, can’t they? There’s always a solution hiding in there, you just have to find it. Let's take a closer look at the equation 2(x - 3) = 8 and uncover the steps to reach the correct answer together.

Step 1: Distributing the 2

Alright, so the first thing we need to do is distribute the 2 on the left side of the equation. It’s kind of like sharing candies; you take 2 candies and give them to each of the friends (the x and the -3) separately. Here’s how it looks:

[ 2(x - 3) = 8 ]

After distributing, we get:

[ 2x - 6 = 8 ]

Pretty straightforward, right? Just remember, distributing is all about breaking it down into smaller parts.

Step 2: Isolating x

Now that we have simplified the equation, it’s time to isolate x. To do this, we need to eliminate -6 from the left side. Think of it like getting rid of some clutter in your room, making room for clarity. We can do this by adding 6 to both sides:

[ 2x - 6 + 6 = 8 + 6 ]

Which simplifies to:

[ 2x = 14 ]

Step 3: Solving for x

This is where the magic happens! To find x, we'll divide both sides by 2. Imagine you have 14 cookies and want to share them with two friends. How many cookies does each friend get? Here’s the math:

[ x = \frac{14}{2} ]

And solving this gives us:

[ x = 7 ]

Wait, What Happened?

Now, before we rush off in excitement shouting, “Eureka!”—there's something we need to point out. The value we found, x = 7, isn’t listed in the original options you provided: A. 5, B. 8, C. 11, D. 14.

What went wrong? Did we make an error? Not exactly! The calculations are solid, but it’s crucial to double-check your question and answer choices. Sometimes, they might not match! Don’t let this discourage you; rather, let it serve as a reminder to always verify your results. This is a key takeaway when preparing for assessments and solving challenges in your mathematics journey.

In Conclusion

Learning to solve equations like 2(x - 3) = 8 means honing not just your math skills, but your attention to detail as well. Next time you encounter an equation, remember the steps we went through: distributing, isolating, and solving—while keeping an eye out for those answer choices.

Math can be challenging, but with a little patience and practice, you’ll find yourself mastering these skills in no time! So, keep practicing, and don’t hesitate to revisit concepts. Every mistake is just another stepping stone on your math journey!

Happy calculating!