Solving (310-n):100=3: A Step-by-Step Guide

Nov 3, 2025 by Admin 44 views

Hey guys! Today, we're diving into solving the equation (310-n):100=3. Don't worry; it's not as intimidating as it looks! We'll break it down step-by-step, making sure you understand each part of the process. Plus, we'll do a verification at the end to ensure our answer is correct. Let's get started!

Understanding the Equation

Before we jump into solving, let's quickly understand what the equation (310-n):100=3 means. This equation involves a variable 'n', and our goal is to find the value of 'n' that makes the equation true. The left side of the equation involves subtracting 'n' from 310, then dividing the result by 100. The right side of the equation is simply 3. To solve this, we need to isolate 'n' on one side of the equation.

Why is this important? Understanding algebraic equations like this is crucial for many areas, including science, engineering, and even everyday problem-solving. Mastering these skills now will set you up for success in future studies and real-world applications. Think of it as building a strong foundation for more complex problem-solving down the road.

Keywords: algebraic equations, variable, isolate, problem-solving

Step-by-Step Solution

Now, let's get our hands dirty and solve this equation! Here’s how we can do it:

Step 1: Isolate the Parenthetical Expression

The first thing we want to do is get rid of that division by 100. To do this, we'll multiply both sides of the equation by 100. This will cancel out the division on the left side:

(310 - n) / 100 = 3

Multiply both sides by 100:

(310 - n) / 100 * 100 = 3 * 100

This simplifies to:

310 - n = 300

Step 2: Isolate the Variable 'n'

Next, we want to isolate 'n'. Currently, 'n' is being subtracted from 310. To get 'n' by itself, we need to subtract 310 from both sides of the equation:

310 - n = 300

Subtract 310 from both sides:

310 - n - 310 = 300 - 310

This simplifies to:

-n = -10

Step 3: Solve for 'n'

We're almost there! We have -n = -10, but we want to find the value of 'n', not '-n'. To do this, we can multiply both sides of the equation by -1:

-n = -10

Multiply both sides by -1:

-n * -1 = -10 * -1

This gives us:

n = 10

So, the solution to the equation (310-n):100=3 is n = 10.

Why is isolating the variable so important? Isolating the variable is a fundamental technique in algebra. It allows us to peel away the layers of the equation and get to the core of what we're trying to solve. Each step we take brings us closer to finding the value of the variable that satisfies the equation. It's like unwrapping a present – each layer reveals more until you finally see what's inside!

Keywords: isolate variable, algebraic manipulation, solving for n

Verification

Now, let's make sure our answer is correct. We'll plug n = 10 back into the original equation and see if it holds true:

Original equation:

(310 - n) / 100 = 3

Substitute n = 10:

(310 - 10) / 100 = 3

Simplify:

300 / 100 = 3

3 = 3

Since the left side of the equation equals the right side, our solution n = 10 is correct!

The importance of verification: Verifying your solution is a critical step in problem-solving. It's like double-checking your work to make sure you haven't made any mistakes. By plugging your solution back into the original equation, you can confirm that it satisfies the equation and that your answer is correct. This not only gives you confidence in your answer but also helps you catch any errors you may have made along the way. Always verify when you can!

Keywords: verifying solutions, checking answers, ensuring accuracy

Alternative Methods

While we solved this equation directly, there are often alternative approaches you can use to tackle similar problems. Here’s one:

Alternative Approach: Working Backwards

Sometimes, you can solve an equation by working backwards. Since (310 - n) / 100 = 3, we know that (310 - n) must equal 3 * 100, which is 300. So, we can rewrite the equation as:

310 - n = 300

From here, we can see that 'n' must be the difference between 310 and 300, which is 10. So, n = 10.

This method can be particularly useful when the equation is relatively simple, and you can easily see the relationships between the numbers.

Why explore alternative methods? Exploring alternative methods isn't just about finding different ways to solve the same problem; it's about deepening your understanding of mathematical concepts. Each method offers a unique perspective and can help you develop a more intuitive understanding of how equations work. Plus, having multiple tools in your toolkit means you'll be better equipped to tackle a wider range of problems in the future. Think of it as expanding your problem-solving horizons!

Keywords: alternative solutions, different approaches, problem-solving skills

Common Mistakes to Avoid

When solving equations, it's easy to make small mistakes that can lead to incorrect answers. Here are a few common mistakes to watch out for:

Forgetting to Distribute: If you have a number multiplying a parenthetical expression, make sure you distribute it to all terms inside the parentheses.
Incorrectly Combining Like Terms: Be careful when combining like terms. Make sure you're only combining terms that have the same variable and exponent.
Not Performing the Same Operation on Both Sides: Remember, whatever you do to one side of the equation, you must do to the other side to maintain equality.
Sign Errors: Pay close attention to signs, especially when dealing with negative numbers.

By being aware of these common mistakes, you can reduce the likelihood of making errors and improve your accuracy when solving equations.

How to avoid mistakes: Preventing errors in math is about more than just knowing the rules; it's about developing good habits. Double-check your work, write neatly, and take your time. If you're unsure about a step, pause and review the concepts involved. It's always better to be careful and accurate than to rush and make mistakes. Remember, practice makes perfect, and with each problem you solve, you'll become more confident and less prone to errors.

Keywords: common mistakes, avoiding errors, math accuracy

Practice Problems

To solidify your understanding, here are a few practice problems you can try:

(250 - x) / 50 = 2
(420 - y) / 200 = 1
(180 - z) / 60 = 2

Try solving these problems on your own, and don't forget to verify your answers!

Why practice is essential: Practice is the key to mastering any skill, and math is no exception. By working through practice problems, you reinforce your understanding of the concepts and techniques involved. Each problem you solve helps you build confidence and develop your problem-solving abilities. So, don't be afraid to tackle those practice problems – they're your ticket to math success!

Keywords: practice problems, math practice, skill development

Conclusion

Alright, guys! We've successfully solved the equation (310-n):100=3 and verified our answer. Remember, the key to solving equations is to break them down into smaller, manageable steps, and always double-check your work. Keep practicing, and you'll become a pro in no time! Happy solving!

Final thoughts: Solving equations is a fundamental skill that can open doors to countless opportunities. From science and engineering to finance and technology, the ability to think critically and solve problems is highly valued in today's world. So, keep learning, keep practicing, and never stop exploring the fascinating world of mathematics. Who knows what amazing things you'll discover along the way!

Keywords: equation solving, math skills, problem-solving abilities