Simplify The Expression: $-10k + 4k$

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms to reduce the complexity of an expression. In this article, we will simplify the expression $-10k + 4k$ using basic algebraic rules.

Understanding the Expression

The given expression is $-10k + 4k$. This expression consists of two terms: $-10k$ and $4k$. Both terms have the same variable, $k$, but they have different coefficients. The coefficient of a term is the numerical value that multiplies the variable.

Like Terms

Like terms are terms that have the same variable raised to the same power. In the expression $-10k + 4k$, both terms have the variable $k$ raised to the power of 1. Therefore, they are like terms.

Simplifying the Expression

To simplify the expression $-10k + 4k$, we need to combine the like terms. We can do this by adding or subtracting the coefficients of the like terms. In this case, we will add the coefficients.

-10k + 4k = (-10 + 4)k

Combining the Coefficients

Now, let's combine the coefficients of the like terms.

-10 + 4 = -6

So, the simplified expression is $-6k$.

Conclusion

In this article, we simplified the expression $-10k + 4k$ using basic algebraic rules. We identified the like terms, combined their coefficients, and arrived at the simplified expression $-6k$. This skill is essential in algebra, as it helps us solve equations and inequalities.

Real-World Applications

Simplifying expressions has numerous real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. By simplifying these expressions, we can better understand the behavior of the objects.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions:

• Identify like terms: Like terms are terms that have the same variable raised to the same power.
• Combine coefficients: Combine the coefficients of like terms by adding or subtracting them.
• Simplify the expression: Simplify the expression by combining like terms and eliminating any unnecessary terms.

Common Mistakes

Here are some common mistakes to avoid when simplifying expressions:

• Not identifying like terms: Failing to identify like terms can lead to incorrect simplifications.
• Not combining coefficients: Failing to combine coefficients can lead to incorrect simplifications.
• Not simplifying the expression: Failing to simplify the expression can lead to incorrect solutions.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

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

Answer Key

Here are the answers to the practice problems:

• $-5x + 3x = -2x$
• $-2y + 4y = 2y$
• $-3z + 2z = -z$

Conclusion

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Introduction

In our previous article, we simplified the expression $-10k + 4k$ using basic algebraic rules. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In the expression $-10k + 4k$, both terms have the variable $k$ raised to the power of 1. Therefore, they are like terms.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable raised to the same power. In the expression $-10k + 4k$, both terms have the variable $k$ raised to the power of 1. Therefore, they are like terms.

Q: How do I combine coefficients?

A: To combine coefficients, add or subtract the coefficients of like terms. In the expression $-10k + 4k$, we add the coefficients to get $-10 + 4 = -6$.

Q: What is the simplified expression for $-10k + 4k$?

A: The simplified expression for $-10k + 4k$ is $-6k$.

Q: Can I simplify expressions with variables of different powers?

A: No, you cannot simplify expressions with variables of different powers. For example, the expression $-10k + 4k^2$ cannot be simplified because the variables have different powers.

Q: Can I simplify expressions with variables of different bases?

A: No, you cannot simplify expressions with variables of different bases. For example, the expression $-10x + 4y$ cannot be simplified because the variables have different bases.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, multiply the numerator and denominator by the least common multiple (LCM) of the denominators. For example, the expression $\frac{-10k}{4} + \frac{4k}{4}$ can be simplified by multiplying the numerator and denominator by 4 to get $-10k + 4k$.

Q: Can I simplify expressions with negative coefficients?

A: Yes, you can simplify expressions with negative coefficients. For example, the expression $-10k + 4k$ can be simplified by combining the coefficients to get $-6k$.

Q: Can I simplify expressions with zero coefficients?

A: Yes, you can simplify expressions with zero coefficients. For example, the expression $-10k + 0k$ can be simplified by eliminating the zero coefficient to get $-10k$.

Conclusion

In conclusion, simplifying expressions is a crucial skill in algebra. By identifying like terms, combining coefficients, and simplifying the expression, we can arrive at the correct solution. With practice and patience, you can master this skill and become proficient in algebra.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

• Simplify the expression $-5x + 3x$.
• Simplify the expression $-2y + 4y$.
• Simplify the expression $-3z + 2z$.
• Simplify the expression $\frac{-10k}{4} + \frac{4k}{4}$.
• Simplify the expression $-10k + 0k$.

Answer Key

Here are the answers to the practice problems:

• $-5x + 3x = -2x$
• $-2y + 4y = 2y$
• $-3z + 2z = -z$
• $\frac{-10k}{4} + \frac{4k}{4} = -6k$
• $-10k + 0k = -10k$