Simplify The Expression By Combining Like Terms: $4x - 6 + X + 4y + 6 - 3$

Introduction

In algebra, combining like terms is a fundamental concept that helps simplify expressions and make them easier to work with. Like terms are terms that have the same variable raised to the same power. In this article, we will simplify the expression $4x - 6 + x + 4y + 6 - 3$ by combining like terms.

Understanding Like Terms

Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. Similarly, $3y$ and $2y$ are like terms because they both have the variable $y$ raised to the power of 1.

Combining Like Terms

To combine like terms, we need to add or subtract the coefficients of the like terms. The coefficient of a term is the number that is multiplied by the variable. For example, in the term $2x$, the coefficient is 2.

Let's simplify the expression $4x - 6 + x + 4y + 6 - 3$ by combining like terms.

Step 1: Identify the Like Terms

The expression contains the following terms:

• $4x$
• $-6$
• $x$
• $4y$
• $6$
• $-3$

We can identify the like terms as follows:

• $4x$ and $x$ are like terms because they both have the variable $x$ raised to the power of 1.
• $4y$ is a like term by itself because it has the variable $y$ raised to the power of 1.
• $-6$ and $6$ are like terms because they both have the same coefficient, which is 6.
• $-3$ is a like term by itself because it has no variable.

Step 2: Combine the Like Terms

Now that we have identified the like terms, we can combine them by adding or subtracting their coefficients.

• $4x$ and $x$ can be combined by adding their coefficients: $4x + x = 5x$
• $4y$ is already a like term by itself, so we don't need to do anything with it.
• $-6$ and $6$ can be combined by adding their coefficients: $-6 + 6 = 0$
• $-3$ is already a like term by itself, so we don't need to do anything with it.

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by removing the terms that have a coefficient of 0.

The simplified expression is:

$5x + 4y - 3$

Conclusion

In this article, we simplified the expression $4x - 6 + x + 4y + 6 - 3$ by combining like terms. We identified the like terms, combined them by adding or subtracting their coefficients, and simplified the expression by removing the terms that have a coefficient of 0. The simplified expression is $5x + 4y - 3$.

Example Problems

Here are some example problems that you can try to practice combining like terms:

• Simplify the expression $2x + 3y - 4x + 2y + 5$
• Simplify the expression $x + 2y - 3x + 4y - 2$
• Simplify the expression $3x - 2y + 4x - 3y + 1$

Tips and Tricks

Here are some tips and tricks that you can use to help you combine like terms:

• Make sure to identify all of the like terms in the expression.
• Use the distributive property to expand the expression and make it easier to identify the like terms.
• Use the commutative property to rearrange the terms in the expression and make it easier to combine the like terms.
• Use the associative property to group the terms in the expression and make it easier to combine the like terms.

Common Mistakes

Here are some common mistakes that you can make when combining like terms:

• Failing to identify all of the like terms in the expression.
• Failing to use the distributive property to expand the expression.
• Failing to use the commutative property to rearrange the terms in the expression.
• Failing to use the associative property to group the terms in the expression.

Real-World Applications

Combining like terms is an important concept in algebra that has many real-world applications. Here are a few examples:

• In physics, combining like terms is used to simplify complex equations that describe the motion of objects.
• In engineering, combining like terms is used to simplify complex equations that describe the behavior of electrical circuits.
• In economics, combining like terms is used to simplify complex equations that describe the behavior of economic systems.

Conclusion

Introduction

Combining like terms is a fundamental concept in algebra that helps simplify expressions and make them easier to work with. In this article, we will answer some frequently asked questions about combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable raised to the same power. You can also use the distributive property to expand the expression and make it easier to identify the like terms.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. The coefficient of a term is the number that is multiplied by the variable. For example, in the term $2x$, the coefficient is 2.

Q: What is the order of operations for combining like terms?

A: The order of operations for combining like terms is as follows:

1. Identify the like terms.
2. Combine the like terms by adding or subtracting their coefficients.
3. Simplify the expression by removing the terms that have a coefficient of 0.

Q: Can I combine unlike terms?

A: No, you cannot combine unlike terms. Unlike terms are terms that have different variables or different powers of the same variable. For example, $2x$ and $3y$ are unlike terms because they have different variables.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms is a specific technique used to simplify expressions by adding or subtracting the coefficients of like terms. Simplifying an expression, on the other hand, is a broader process that involves combining like terms, removing unnecessary terms, and rearranging the terms in the expression.

Q: How do I know when to combine like terms?

A: You should combine like terms whenever you have an expression that contains multiple terms with the same variable raised to the same power. Combining like terms can help simplify the expression and make it easier to work with.

Q: Can I use a calculator to combine like terms?

A: Yes, you can use a calculator to combine like terms. However, it's always a good idea to check your work by hand to make sure that you have combined the like terms correctly.

Q: What are some common mistakes to avoid when combining like terms?

A: Some common mistakes to avoid when combining like terms include:

• Failing to identify all of the like terms in the expression.
• Failing to use the distributive property to expand the expression.
• Failing to use the commutative property to rearrange the terms in the expression.
• Failing to use the associative property to group the terms in the expression.

Q: How do I practice combining like terms?

A: You can practice combining like terms by working through example problems and exercises. You can also use online resources and practice tests to help you improve your skills.

Conclusion

In conclusion, combining like terms is an important concept in algebra that helps simplify expressions and make them easier to work with. By identifying the like terms, combining them by adding or subtracting their coefficients, and simplifying the expression by removing the terms that have a coefficient of 0, we can simplify complex expressions and make them easier to understand.