Simplify The Expression: $3x - 30$

$$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to solve equations and inequalities more efficiently. It involves combining like terms and eliminating any unnecessary components from the expression. In this article, we will focus on simplifying the expression $3x - 30$.

Understanding the Expression

The given expression is $3x - 30$. This is a linear expression, which means it is a polynomial of degree one. The expression consists of two terms: $3x$ and $-30$. The first term is a product of a constant and a variable, while the second term is a constant.

Simplifying the Expression

To simplify the expression $3x - 30$, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: $3x$ and $-30$. However, $-30$ is a constant term, and it does not have a variable. Therefore, we cannot combine it with $3x$.

Factoring Out the GCF

However, we can factor out the greatest common factor (GCF) from the expression. The GCF of $3x$ and $-30$ is $3$. We can factor out $3$ from both terms:

$$3x - 30 = 3(x - 10)$$

Explanation

In the above expression, we have factored out $3$ from both terms. This is done by dividing each term by $3$. The resulting expression is $3(x - 10)$.

Why Simplify the Expression?

Simplifying the expression $3x - 30$ has several benefits. Firstly, it makes the expression easier to read and understand. Secondly, it helps us to identify any common factors that can be factored out. Finally, it makes it easier to solve equations and inequalities involving the expression.

Real-World Applications

Simplifying expressions like $3x - 30$ has many real-world applications. For example, in physics, we often encounter expressions that involve the product of a constant and a variable. Simplifying these expressions helps us to solve problems more efficiently.

Conclusion

In conclusion, simplifying the expression $3x - 30$ involves combining like terms and factoring out the greatest common factor. This helps us to identify any common factors that can be factored out and makes the expression easier to read and understand. By simplifying expressions like $3x - 30$, we can solve equations and inequalities more efficiently and make it easier to apply mathematical concepts to real-world problems.

Example Problems

Problem 1

Simplify the expression $4x - 20$.

Solution

To simplify the expression $4x - 20$, we need to combine like terms. However, $-20$ is a constant term, and it does not have a variable. Therefore, we cannot combine it with $4x$. However, we can factor out the greatest common factor (GCF) from the expression. The GCF of $4x$ and $-20$ is $4$. We can factor out $4$ from both terms:

$$4x - 20 = 4(x - 5)$$

Problem 2

Simplify the expression $2x + 10$.

Solution

To simplify the expression $2x + 10$, we need to combine like terms. However, $10$ is a constant term, and it does not have a variable. Therefore, we cannot combine it with $2x$. However, we can factor out the greatest common factor (GCF) from the expression. The GCF of $2x$ and $10$ is $2$. We can factor out $2$ from both terms:

$$2x + 10 = 2(x + 5)$$

Tips and Tricks

Tip 1

When simplifying expressions, always look for common factors that can be factored out.

Tip 2

When combining like terms, make sure to combine terms with the same variable raised to the same power.

Tip 3

When factoring out the greatest common factor, make sure to divide each term by the GCF.

Common Mistakes

Mistake 1

Not combining like terms when simplifying expressions.

Mistake 2

Not factoring out the greatest common factor when simplifying expressions.

Mistake 3

Not checking for common factors that can be factored out.

Conclusion

$$$$ $$

Introduction

In our previous article, we discussed how to simplify the expression $3x - 30$. In this article, we will answer some frequently asked questions related to simplifying expressions like $3x - 30$.

Q&A

Q1: What is the greatest common factor (GCF) of $3x$ and $-30$?

A1: The greatest common factor (GCF) of $3x$ and $-30$ is $3$.

Q2: How do I simplify the expression $4x - 20$?

A2: To simplify the expression $4x - 20$, you need to combine like terms. However, $-20$ is a constant term, and it does not have a variable. Therefore, you cannot combine it with $4x$. However, you can factor out the greatest common factor (GCF) from the expression. The GCF of $4x$ and $-20$ is $4$. You can factor out $4$ from both terms:

$$4x - 20 = 4(x - 5)$$

Q3: What is the difference between combining like terms and factoring out the greatest common factor?

A3: Combining like terms involves adding or subtracting terms with the same variable raised to the same power. Factoring out the greatest common factor involves dividing each term by the GCF.

Q4: How do I check if there are any common factors that can be factored out?

A4: To check if there are any common factors that can be factored out, you need to look for terms that have a common factor. For example, in the expression $6x + 12$, the terms $6x$ and $12$ have a common factor of $6$. You can factor out $6$ from both terms:

$$6x + 12 = 6(x + 2)$$

Q5: What are some common mistakes to avoid when simplifying expressions?

A5: Some common mistakes to avoid when simplifying expressions include:

• Not combining like terms
• Not factoring out the greatest common factor
• Not checking for common factors that can be factored out

Tips and Tricks

Tip 1

When simplifying expressions, always look for common factors that can be factored out.

Tip 2

When combining like terms, make sure to combine terms with the same variable raised to the same power.

Tip 3

When factoring out the greatest common factor, make sure to divide each term by the GCF.

Real-World Applications

Simplifying expressions like $3x - 30$ has many real-world applications. For example, in physics, we often encounter expressions that involve the product of a constant and a variable. Simplifying these expressions helps us to solve problems more efficiently.

Conclusion

In conclusion, simplifying expressions like $3x - 30$ involves combining like terms and factoring out the greatest common factor. This helps us to identify any common factors that can be factored out and makes the expression easier to read and understand. By simplifying expressions like $3x - 30$, we can solve equations and inequalities more efficiently and make it easier to apply mathematical concepts to real-world problems.

Example Problems

Problem 1

Simplify the expression $2x + 10$.

Solution

To simplify the expression $2x + 10$, you need to combine like terms. However, $10$ is a constant term, and it does not have a variable. Therefore, you cannot combine it with $2x$. However, you can factor out the greatest common factor (GCF) from the expression. The GCF of $2x$ and $10$ is $2$. You can factor out $2$ from both terms:

$$2x + 10 = 2(x + 5)$$

Problem 2

Simplify the expression $3x - 15$.

Solution

To simplify the expression $3x - 15$, you need to combine like terms. However, $-15$ is a constant term, and it does not have a variable. Therefore, you cannot combine it with $3x$. However, you can factor out the greatest common factor (GCF) from the expression. The GCF of $3x$ and $-15$ is $3$. You can factor out $3$ from both terms:

$$3x - 15 = 3(x - 5)$$

Common Mistakes

Mistake 1

Not combining like terms when simplifying expressions.

Mistake 2

Not factoring out the greatest common factor when simplifying expressions.

Mistake 3

Not checking for common factors that can be factored out.

Conclusion

In conclusion, simplifying expressions like $3x - 30$ involves combining like terms and factoring out the greatest common factor. This helps us to identify any common factors that can be factored out and makes the expression easier to read and understand. By simplifying expressions like $3x - 30$, we can solve equations and inequalities more efficiently and make it easier to apply mathematical concepts to real-world problems.