What Is 10x - 8 + 3 - 4x + 6x Equal To? Let’s Break It Down!

Natalia Schneider 21 May 2025

Alright folks, if you’ve ever been scratching your head over math problems like "what is 10x - 8 + 3 - 4x + 6x equal to?" you’re not alone. Math can be tricky, but don’t worry, we’ve got you covered! Whether you’re a student trying to ace your algebra homework or just brushing up on your math skills, understanding expressions like this is key. In this article, we’ll break it down step by step, making it super easy for you to grasp.

Let’s face it, math isn’t everyone’s favorite subject, but it’s an essential part of life. From calculating tips at a restaurant to figuring out your monthly budget, math plays a huge role in our daily lives. And when it comes to algebra, expressions like 10x - 8 + 3 - 4x + 6x might seem intimidating at first glance. But trust me, once you get the hang of it, it’s not that bad.

So, why are we focusing on this particular expression? Well, because it’s a great example of how to simplify algebraic equations. By the end of this article, you’ll not only know the answer to this question but also how to tackle similar problems in the future. Ready to dive in? Let’s go!

Understanding the Basics of Algebraic Expressions

Before we jump into solving 10x - 8 + 3 - 4x + 6x, let’s take a quick look at what algebraic expressions are. Simply put, an algebraic expression is a mathematical phrase that combines numbers, variables (like x), and operation symbols (+, -, *, /). Think of it as a recipe for solving math problems. Each part of the expression plays a role in determining the final result.

What Makes Up an Algebraic Expression?

Variables: These are symbols (usually letters) that represent unknown values, like x or y.
Coefficients: These are the numbers that multiply the variables, like the 10 in 10x.
Constants: These are fixed numbers in the expression, like -8 or +3.
Operators: These are the symbols that tell you what to do with the numbers and variables, like +, -, *, or /.

Now that we’ve got the basics down, let’s move on to the next step: simplifying the expression.

Simplifying 10x - 8 + 3 - 4x + 6x

Simplifying an algebraic expression means combining like terms to make it easier to work with. In our case, we’re dealing with the expression 10x - 8 + 3 - 4x + 6x. Let’s break it down step by step.

Step 1: Group the Like Terms

First things first, we need to group the terms that are alike. In this expression, we have three types of terms:

Terms with x: 10x, -4x, and 6x
Constant terms: -8 and +3

By grouping the like terms, we get:

(10x - 4x + 6x) + (-8 + 3)

Step 2: Combine the Like Terms

Now that we’ve grouped the like terms, it’s time to combine them. Let’s start with the terms that have x:

10x - 4x + 6x = 12x

Next, let’s combine the constant terms:

-8 + 3 = -5

So, our simplified expression becomes:

12x - 5

Why Simplifying is Important

Simplifying algebraic expressions is crucial because it makes solving equations much easier. Imagine trying to solve a complex equation without simplifying it first. It would be like trying to put together a puzzle with all the pieces scattered around. Simplifying helps you organize the pieces, making it easier to see the big picture.

Real-World Applications

Algebra isn’t just something you learn in school; it has real-world applications. For example, if you’re planning a road trip and need to calculate how much gas you’ll need, algebra can help. Or if you’re trying to figure out how much money you’ll save by switching to a different phone plan, algebra can give you the answer. Simplifying expressions is a key part of solving these types of problems.

Common Mistakes to Avoid

When working with algebraic expressions, it’s easy to make mistakes. Here are a few common ones to watch out for:

Forgetting to combine like terms: Always double-check that you’ve grouped and combined all the terms that are alike.
Mixing up positive and negative signs: Pay close attention to the signs (+ or -) when combining terms. A small mistake here can throw off your entire calculation.
Not following the order of operations: Remember PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule ensures that you’re solving the expression in the correct order.

By avoiding these mistakes, you’ll be well on your way to mastering algebraic expressions.

How to Check Your Work

Once you’ve simplified an expression, it’s always a good idea to double-check your work. Here’s how you can do that:

Substitute a Value for x

Choose a random number for x, say x = 2, and substitute it into both the original expression and the simplified expression. If both give you the same result, you’ve done it right!

Original expression: 10(2) - 8 + 3 - 4(2) + 6(2) = 20 - 8 + 3 - 8 + 12 = 19

Simplified expression: 12(2) - 5 = 24 - 5 = 19

Since both results are the same, you know you’ve simplified correctly.

Additional Tips for Solving Algebraic Expressions

Here are a few extra tips to help you tackle algebraic expressions with confidence:

Practice makes perfect: The more you practice, the better you’ll get at simplifying expressions.
Use online resources: There are tons of great websites and apps out there that can help you practice and improve your algebra skills.
Ask for help: If you’re stuck, don’t hesitate to ask a teacher, tutor, or classmate for help.

Remember, everyone learns at their own pace. Don’t get discouraged if it takes you a little longer to master algebra. With time and practice, you’ll get there!

Conclusion

So, there you have it! The answer to "what is 10x - 8 + 3 - 4x + 6x equal to?" is 12x - 5. By following the steps we outlined, you can simplify any algebraic expression with ease. Remember to group and combine like terms, watch out for common mistakes, and always double-check your work.

Now it’s your turn! Try simplifying a few expressions on your own and see how you do. And if you have any questions or need further clarification, feel free to leave a comment below. Happy math-ing!

Understanding the Basics of Algebraic Expressions
Simplifying 10x - 8 + 3 - 4x + 6x
Step 1: Group the Like Terms
Step 2: Combine the Like Terms
Why Simplifying is Important
Real-World Applications
Common Mistakes to Avoid
How to Check Your Work
Additional Tips for Solving Algebraic Expressions
Conclusion

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