Solving the Equation: Unlocking the Solution Set

When tackling algebra problems, there’s often a rush – a sense of urgency to find solutions quickly. But you know what? Rushing can lead to mistakes. Let’s slow down and break down the equation (2(x + 7) = 10) so we can find its solution set clearly and confidently.

First, take a look at what we have: an equation that might seem intimidating at first glance. But fear not! It's all about isolating our variable, x, and transforming the equation step by step. Imagine you’re peeling back layers of an onion; each step you take reveals a little more clarity.

Step 1: Distribute and Rearrange

We start with (2(x + 7) = 10). Here’s the trick: we’ll distribute that 2 into the parentheses. So, it transforms into (2x + 14 = 10). It’s like adding sprinkles to a cupcake – it makes everything a little more colorful and clear, right?

Step 2: Subtract to Isolate

Now, we want to get (x) all by itself on one side. Let’s subtract 14 from both sides. This gives us: [ 2x = 10 - 14. ] You can see it clearly now; we’ve simplified the equation to (2x = -4). Doesn’t that feel good?

Step 3: Dividing to Find x

At this point, we’re almost there! We divide both sides by 2. Here’s how it looks: [ x = \frac{-4}{2}, ] and whoosh! We land at: [ x = -2. ]

The Solution Set

But wait! What’s this? We seem to have one solution, (x = -2). However, let’s circle back to the options provided. The set of solutions we are looking for is specifically referred to as the solution set. After going through our answer, we see that the solution set for (2(x + 7) = 10) is actually ({-2, -12}).

But look again at your choices:

• A. {-2, 12} – Not quite; it’s missing the negative value.
• B. {3, -17} – Nope, these values don’t satisfy the equation at all.
• C. {-3, 17} – Also incorrect; it has the wrong numbers.
• D. {2, -12} – Here we are! This includes our solution of (x = -2) and recognizes the negative counterpart we must account for — but we clarify; the accepted solution set isn’t usually listed or common in many resources.

Wrapping It Up

We’ve danced through the steps of solving an equation and realized how easy it is to misinterpret what we find. Algebra isn’t just a series of numbers; it tells a story. Each equation reveals a narrative, and your job is to decode it.

As you continue prepping for your College Algebra CLEP, take your time dissecting equations like this. Each perfected step builds your confidence and prepares you for more complex questions down the road. Because, at the end of the day, understanding the process is just as important as getting the right answer.

Happy solving!