Select The Simplified Form Of This Expression: X + 4 7 + 5 X \frac{x+4}{7} + 5x 7 X + 4 ​ + 5 X

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 simplifying the given expression: $\frac{x+4}{7} + 5x$. We will break down the process into manageable steps, making it easy to understand and follow along.

Understanding the Expression

Before we dive into simplifying the expression, let's take a closer look at what we're dealing with. The given expression is a combination of two terms: $\frac{x+4}{7}$ and $5x$. The first term is a fraction, while the second term is a polynomial. Our goal is to simplify this expression by combining like terms and eliminating any unnecessary components.

Step 1: Simplify the Fraction

The first step in simplifying the expression is to focus on the fraction: $\frac{x+4}{7}$. At this point, we can't simplify the fraction further, as there are no common factors between the numerator and the denominator. However, we can rewrite the fraction in a more manageable form by multiplying both the numerator and the denominator by 7:

$$\frac{x+4}{7} = \frac{7(x+4)}{7 \cdot 7} = \frac{7x + 28}{49}$$

Step 2: Combine Like Terms

Now that we have simplified the fraction, let's focus on combining like terms. The expression now looks like this:

$$\frac{7x + 28}{49} + 5x$$

We can see that the first term, $\frac{7x + 28}{49}$, has a common factor of $x$ with the second term, $5x$. We can rewrite the expression as:

$$\frac{7x + 28}{49} + 5x = \frac{7x + 28}{49} + \frac{5x \cdot 49}{49}$$

Step 3: Eliminate the Fraction

Now that we have combined like terms, let's eliminate the fraction by multiplying both the numerator and the denominator by 49:

$$\frac{7x + 28}{49} + \frac{5x \cdot 49}{49} = \frac{7x + 28 + 245x}{49}$$

Step 4: Simplify the Expression

The final step in simplifying the expression is to combine like terms and eliminate any unnecessary components. We can rewrite the expression as:

$$\frac{7x + 28 + 245x}{49} = \frac{252x + 28}{49}$$

However, we can simplify this expression further by factoring out the common factor of 28:

$$\frac{252x + 28}{49} = \frac{28(9x + 1)}{49}$$

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By breaking down the process into manageable steps, we can make it easy to understand and follow along. In this article, we focused on simplifying the expression: $\frac{x+4}{7} + 5x$. We broke down the process into four steps: simplifying the fraction, combining like terms, eliminating the fraction, and simplifying the expression. By following these steps, we were able to simplify the expression and arrive at the final answer.

Final Answer

The final answer is: $\boxed{\frac{28(9x + 1)}{49}}$

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Simplifying Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Simplifying Algebraic Expressions

Frequently Asked Questions

Q: What is the first step in simplifying an algebraic expression? A: The first step in simplifying an algebraic expression is to simplify the fraction, if present.

Q: How do I combine like terms in an algebraic expression? A: To combine like terms, look for common factors between the numerator and the denominator, and then multiply both the numerator and the denominator by that factor.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to simplify the fraction, if present. This involves rewriting the fraction in a more manageable form by multiplying both the numerator and the denominator by a common factor.

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, look for common factors between the numerator and the denominator, and then multiply both the numerator and the denominator by that factor. This will allow you to rewrite the expression in a simpler form.

Q: What is the difference between simplifying and solving an algebraic expression?

A: Simplifying an algebraic expression involves rewriting the expression in a simpler form, while solving an algebraic expression involves finding the value of the variable that makes the expression true.

Q: Can I simplify an algebraic expression with multiple fractions?

A: Yes, you can simplify an algebraic expression with multiple fractions by following the same steps as before. First, simplify each fraction individually, and then combine like terms.

Q: How do I know when to simplify an algebraic expression?

A: You should simplify an algebraic expression whenever possible, as it can make the expression easier to work with and understand. This is especially true when working with complex expressions or when trying to solve for a variable.

Q: Can I use a calculator to simplify an algebraic expression?

A: Yes, you can use a calculator to simplify an algebraic expression. However, keep in mind that calculators may not always provide the simplest form of the expression, so it's a good idea to double-check your work.

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

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not simplifying fractions before combining like terms
• Not combining like terms correctly
• Not eliminating unnecessary components
• Not checking your work for errors

Q: How do I know if I have simplified an algebraic expression correctly?

A: To check if you have simplified an algebraic expression correctly, try the following:

• Plug in a value for the variable and see if the expression evaluates to a true statement
• Check if the expression is in its simplest form
• Compare your work to a known solution or a reference solution

Q: Can I simplify an algebraic expression with variables in the denominator?

A: Yes, you can simplify an algebraic expression with variables in the denominator. However, you will need to follow special rules to avoid dividing by zero.

Q: How do I simplify an algebraic expression with multiple variables?

A: To simplify an algebraic expression with multiple variables, follow the same steps as before. First, simplify each variable individually, and then combine like terms.

Q: Can I simplify an algebraic expression with absolute values?

A: Yes, you can simplify an algebraic expression with absolute values. However, you will need to follow special rules to handle the absolute value correctly.

Q: How do I simplify an algebraic expression with exponents?

A: To simplify an algebraic expression with exponents, follow the same steps as before. First, simplify each exponent individually, and then combine like terms.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By following the steps outlined in this article and avoiding common mistakes, you can simplify even the most complex expressions. Remember to always check your work and to use a calculator when necessary. With practice and patience, you will become a master of simplifying algebraic expressions.