First, Rewrite The Expression By Combining Like Terms.$\frac{1}{2}(13x + 5x - 6 - 8x + 14) = \frac{1}{2}(\square X + \square$\]

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on rewriting an expression by combining like terms, a crucial step in simplifying algebraic expressions. We will use the given expression $\frac{1}{2}(13x + 5x - 6 - 8x + 14)$ as an example and guide you through the process of simplifying it.

Understanding Like Terms

Before we dive into simplifying the expression, let's first understand what like terms are. Like terms are terms that have the same variable raised to the same power. In other words, they are terms that have the same base and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Rewriting the Expression

Now that we understand like terms, let's rewrite the given expression by combining like terms.

$\frac{1}{2}(13x + 5x - 6 - 8x + 14)$

To rewrite this expression, we need to combine the like terms. The like terms in this expression are the terms with the variable $x$. We can combine these terms by adding their coefficients.

Combining Like Terms

Let's combine the like terms in the expression.

$\frac{1}{2}(13x + 5x - 8x + 14 - 6)$

Now, let's simplify the expression by combining the like terms.

$\frac{1}{2}(13x + 5x - 8x + 14 - 6)$

$= \frac{1}{2}(10x + 8)$

$= \frac{1}{2} \times 10x + \frac{1}{2} \times 8$

$= 5x + 4$

Therefore, the simplified expression is $\frac{1}{2}(13x + 5x - 6 - 8x + 14) = 5x + 4$.

Conclusion

In this article, we learned how to rewrite an expression by combining like terms. We used the given expression $\frac{1}{2}(13x + 5x - 6 - 8x + 14)$ as an example and guided you through the process of simplifying it. We learned that like terms are terms that have the same variable raised to the same power and that combining like terms involves adding their coefficients. By following these steps, you can simplify any algebraic expression by combining like terms.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions by combining like terms:

• Identify like terms: The first step in simplifying an algebraic expression is to identify the like terms. Look for terms with the same variable raised to the same power.
• Combine like terms: Once you have identified the like terms, combine them by adding their coefficients.
• Simplify the expression: After combining the like terms, simplify the expression by combining any remaining like terms.
• Check your work: Finally, check your work by plugging the simplified expression back into the original equation.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying algebraic expressions by combining like terms:

• Not identifying like terms: Failing to identify like terms can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying the expression: Failing to simplify the expression can lead to incorrect simplifications.
• Not checking your work: Failing to check your work can lead to incorrect simplifications.

Real-World Applications

Simplifying algebraic expressions by combining like terms has many real-world applications. Here are a few examples:

• Science: Simplifying algebraic expressions is essential in science, where equations are used to model real-world phenomena.
• Engineering: Simplifying algebraic expressions is essential in engineering, where equations are used to design and optimize systems.
• Finance: Simplifying algebraic expressions is essential in finance, where equations are used to model financial systems and make predictions about future outcomes.

Conclusion

Introduction

In our previous article, we discussed how to simplify algebraic expressions by combining like terms. In this article, we will answer some frequently asked questions about simplifying algebraic expressions by combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In other words, they are terms that have the same base and exponent. 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, look for terms with the same variable raised to the same power. For example, in the expression $2x + 5x - 3x$, the like terms are $2x$, $5x$, and $-3x$ because they all have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add their coefficients. For example, in the expression $2x + 5x - 3x$, the like terms are $2x$, $5x$, and $-3x$. To combine these terms, add their coefficients: $2 + 5 - 3 = 4$. Therefore, the simplified expression is $4x$.

Q: What if I have a term with a negative coefficient?

A: If you have a term with a negative coefficient, you can still combine it with other like terms. For example, in the expression $2x - 5x + 3x$, the like terms are $2x$, $-5x$, and $3x$. To combine these terms, add their coefficients: $2 - 5 + 3 = 0$. Therefore, the simplified expression is $0x$, which is equal to $0$.

Q: Can I simplify an expression with variables raised to different powers?

A: No, you cannot simplify an expression with variables raised to different powers. For example, in the expression $2x^2 + 5x - 3x^3$, the terms $2x^2$ and $-3x^3$ have different powers of $x$. Therefore, you cannot combine them.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you can multiply the numerator and denominator of each fraction by the least common multiple (LCM) of the denominators. For example, in the expression $\frac{2x}{3} + \frac{5x}{6}$, the LCM of the denominators is $6$. Therefore, you can multiply the numerator and denominator of each fraction by $6$: $\frac{2x \times 6}{3 \times 6} + \frac{5x \times 6}{6 \times 6} = \frac{12x}{18} + \frac{30x}{36}$. Now, you can combine the like terms: $\frac{12x}{18} + \frac{30x}{36} = \frac{4x}{6} + \frac{5x}{6} = \frac{9x}{6}$.

Q: Can I simplify an expression with parentheses?

A: Yes, you can simplify an expression with parentheses. To simplify an expression with parentheses, you can distribute the terms inside the parentheses to the terms outside the parentheses. For example, in the expression $2(x + 3)$, you can distribute the $2$ to the terms inside the parentheses: $2x + 6$.

Conclusion

In conclusion, simplifying algebraic expressions by combining like terms is an essential skill for any math enthusiast. By following the steps outlined in this article, you can simplify any algebraic expression by combining like terms. Remember to identify like terms, combine like terms, simplify the expression, and check your work. With practice and patience, you will become proficient in simplifying algebraic expressions by combining like terms.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions by combining like terms:

• Use a calculator: If you are having trouble simplifying an expression, try using a calculator to check your work.
• Check your work: Always check your work by plugging the simplified expression back into the original equation.
• Use a diagram: If you are having trouble identifying like terms, try using a diagram to visualize the expression.
• Practice, practice, practice: The more you practice simplifying algebraic expressions by combining like terms, the more proficient you will become.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying algebraic expressions by combining like terms:

• Not identifying like terms: Failing to identify like terms can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
• Not simplifying the expression: Failing to simplify the expression can lead to incorrect simplifications.
• Not checking your work: Failing to check your work can lead to incorrect simplifications.