Equation With Solution Set {-3}: Find The Right One!

Hey Plastik Magazine readers! Ever feel like math problems are just cryptic puzzles waiting to be solved? Well, today we're diving into one that's all about finding the right equation. We've got a solution set, {-3}, and our mission, should we choose to accept it (and we do!), is to figure out which equation from the options has this very solution. It might sound intimidating, but don't worry, we'll tackle this together, step by step. So, grab your thinking caps, and let's get started!

The Challenge: Finding the Perfect Fit

Okay, so the core of this problem revolves around understanding what a 'solution set' actually means. In simple terms, a solution set is just a collection of values that make an equation true. In our case, the solution set is {-3}, which means we're looking for an equation that becomes a true statement when we substitute x with -3. To nail this, we're going to have to test each equation, plugging in -3 for x and seeing if the left side equals the right side. It's like a mathematical version of Cinderella, but instead of a glass slipper, we're looking for the perfect equation fit! This might seem tedious, but it's a super straightforward way to solve this kind of problem. Remember, patience and careful calculation are your best friends here. We're not just guessing; we're systematically checking each option to find the one that works. Let's put on our detective hats and start investigating these equations!

Option A: 4x - 8 = 4

Let's kick things off with the first contender: 4x - 8 = 4. To see if -3 is a solution, we'll substitute x with -3 in the equation. This gives us 4(-3) - 8 = 4. Now, let's simplify the left side. 4 multiplied by -3 is -12, so we have -12 - 8 = 4. Subtracting 8 from -12 gives us -20. So, our equation now looks like -20 = 4. Uh oh! This is definitely not a true statement. -20 is way different from 4. This means that -3 is not a solution for this equation. Option A is out! We can cross this one off our list and move on to the next equation. Remember, even though this one didn't work out, the process of substitution is key. We're building our understanding of how to verify solutions, and that's a valuable skill in math. Don't get discouraged; we've still got other options to explore!

Option B: 4x - 8 = -4

Alright, let's move on to Option B: 4x - 8 = -4. Just like before, our mission is to substitute x with -3 and see if the equation holds true. So, we replace x with -3, which gives us 4(-3) - 8 = -4. Let's simplify the left side again. 4 times -3 is -12, so we have -12 - 8 = -4. Now, subtracting 8 from -12, we get -20. The equation now reads -20 = -4. Hmm, still not a match! -20 is not equal to -4. This means -3 is not a solution for Option B either. Two down, and we're learning more with each step. Even though these equations haven't worked out, the process of plugging in the solution and simplifying is crucial. We're reinforcing the fundamental skill of equation verification. Don't lose heart, guys! We've got two more options to check. The perfect equation might just be waiting for us!

Option C: 4x + 8 = -4

Okay, time to tackle Option C: 4x + 8 = -4. You know the drill by now! We're substituting x with -3. This gives us 4(-3) + 8 = -4. Let's simplify that left side. 4 multiplied by -3 is -12, so the equation becomes -12 + 8 = -4. Now, adding 8 to -12, we get -4. So, the equation now reads -4 = -4. Bingo! We've got a match! -4 is indeed equal to -4. This means that -3 is a solution for Option C. We found our Cinderella equation! Option C is looking pretty good right now, but just to be absolutely sure, and to practice our skills, let's check the last option as well. We want to be 100% confident in our answer. Plus, checking the last option gives us more practice with substitution and simplification, which is always a win!

Option D: 4x + 8 = 4

Last but not least, let's investigate Option D: 4x + 8 = 4. As always, we substitute x with -3, giving us 4(-3) + 8 = 4. Time to simplify! 4 times -3 is -12, so we have -12 + 8 = 4. Adding 8 to -12 gives us -4. The equation now looks like -4 = 4. Nope! This is not a true statement. -4 is definitely not equal to 4. This confirms that -3 is not a solution for Option D. So, after checking all the options, we have a clear winner.

The Verdict: Option C is the Champion!

So, after carefully analyzing each equation, we've discovered that Option C, 4x + 8 = -4, is the equation that has the solution set {-3}. We did it, guys! By substituting -3 for x in each equation, we were able to determine which one held true. This problem highlights the importance of understanding what a solution set means and how to verify solutions. Remember, the key is to substitute the value from the solution set into the equation and see if it creates a true statement. It's a methodical process, but it's a powerful tool for solving equations. You've tackled this problem like pros, and hopefully, you feel a little more confident in your equation-solving abilities now. Keep practicing, and those mathematical puzzles will become less puzzling in no time!

Key takeaway: When you're faced with a problem like this, don't be afraid to dive in and test each option. Substitution is your friend! And remember, even if the first few options don't work out, you're still gaining valuable practice and knowledge along the way. Now go forth and conquer more math challenges!