Solving -2x + 3 = -15 Find The Value Of X

Hey everyone! Today, we're diving deep into a fundamental algebraic problem: solving for x in the equation -2x + 3 = -15. This is a classic example that you'll encounter frequently in mathematics, so mastering it is super important. We'll break it down step-by-step, making sure you understand not just the how, but also the why behind each operation. So, grab your pencils and notebooks, and let's get started!

Understanding the Basics

Before we jump into the solution, let's quickly review some key concepts. In algebra, our goal is often to isolate a variable (in this case, x) on one side of the equation. Think of it like peeling away layers of an onion – we want to get x all by itself. To do this, we use inverse operations. Remember, whatever you do to one side of the equation, you must do to the other to maintain the balance. This is the golden rule of algebra!

What are Inverse Operations?

Inverse operations are operations that "undo" each other. Here are a few examples:

• The inverse of addition is subtraction, and vice versa.
• The inverse of multiplication is division, and vice versa.

We'll be using these inverse operations to isolate x in our equation. Now, let's tackle the problem step-by-step.

Step-by-Step Solution: -2x + 3 = -15

Step 1: Isolate the Term with x

Our first goal is to get the term with x (-2x) by itself on one side of the equation. To do this, we need to get rid of the +3. The inverse operation of addition is subtraction, so we'll subtract 3 from both sides of the equation:

-2x + 3 - 3 = -15 - 3

This simplifies to:

-2x = -18

Great! We've successfully isolated the term with x. Now, let's move on to the next step.

Step 2: Isolate x

Now we have -2x = -18. Remember, -2x means -2 multiplied by x. The inverse operation of multiplication is division, so we'll divide both sides of the equation by -2:

-2x / -2 = -18 / -2

This simplifies to:

x = 9

And there you have it! We've solved for x. The value of x that makes the equation true is 9.

Verifying the Solution

It's always a good idea to check your answer to make sure it's correct. To do this, we'll substitute our solution (x = 9) back into the original equation and see if it holds true:

-2(9) + 3 = -15

Let's simplify:

-18 + 3 = -15

-15 = -15

It checks out! Our solution is correct. x = 9 is indeed the value that makes the equation true.

Common Mistakes to Avoid

When solving equations like this, there are a few common mistakes that students often make. Let's go over them so you can avoid these pitfalls:

1. Forgetting to apply the operation to both sides: Remember, the golden rule! Whatever you do to one side of the equation, you must do to the other. If you only subtract 3 from the left side in Step 1, you'll throw off the balance and get the wrong answer.
2. Incorrectly applying inverse operations: Make sure you're using the correct inverse operation. For example, if the equation involves addition, you need to subtract; if it involves multiplication, you need to divide.
3. Making sign errors: Pay close attention to the signs (positive and negative) of the numbers. A simple sign error can lead to an incorrect solution. For example, dividing -18 by -2 gives you a positive 9, not a negative 9.
4. Not following the order of operations (PEMDAS/BODMAS): When verifying your solution, remember to follow the order of operations (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). This will ensure you're simplifying the equation correctly.

By being mindful of these common mistakes, you can improve your accuracy and confidence in solving algebraic equations.

Practice Problems

Now that we've worked through this example together, let's try a few practice problems to solidify your understanding. Solving math problems is like building a muscle – the more you practice, the stronger you become!

Here are a few problems for you to try:

1. 3x - 5 = 10
2. -4x + 7 = -13
3. 2x + 1 = 9

Work through these problems step-by-step, just like we did in the example. Remember to isolate the term with x first, and then isolate x itself. And don't forget to verify your solutions!

Real-World Applications

You might be wondering, "When will I ever use this in the real world?" Well, solving for x is a fundamental skill that has applications in many different fields. Here are just a few examples:

• Engineering: Engineers use algebraic equations to design structures, calculate forces, and solve various problems related to physics and mechanics.
• Finance: Financial analysts use equations to calculate interest rates, loan payments, and investment returns.
• Computer Science: Programmers use algebraic equations to develop algorithms and solve computational problems.
• Everyday Life: Even in everyday situations, you might use algebraic thinking to solve problems. For example, if you're trying to figure out how much to charge for a service you're providing, you might use an equation to calculate your costs and desired profit.

So, while it might seem abstract now, mastering algebra will open doors to many opportunities in the future.

Conclusion

Alright, guys! We've covered a lot in this guide. We've learned how to solve for x in the equation -2x + 3 = -15, discussed the importance of inverse operations, identified common mistakes to avoid, and even explored some real-world applications of algebra. The key takeaway is that solving algebraic equations is a step-by-step process that requires careful attention to detail and a solid understanding of the basic principles.

Remember, practice makes perfect! The more you work through these types of problems, the more comfortable and confident you'll become. Don't be afraid to make mistakes – they're a valuable learning opportunity. And most importantly, have fun with it! Math can be challenging, but it can also be incredibly rewarding.

So, keep practicing, keep learning, and keep exploring the wonderful world of mathematics! You've got this!