Simplify:${-6w - 4(-2x + 7w) + 3x}$

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Introduction to Simplifying Algebraic Expressions

Simplifying algebraic expressions is a crucial skill in mathematics, particularly in algebra and calculus. It involves combining like terms and eliminating any unnecessary components to make the expression more manageable and easier to work with. In this article, we will focus on simplifying a given algebraic expression using the distributive property and combining like terms.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand and simplify expressions by multiplying each term inside the parentheses with the term outside. In the given expression, we have a term $-4(-2x + 7w)$, which can be simplified using the distributive property.

Applying the Distributive Property

To simplify the expression $-4(-2x + 7w)$, we need to multiply each term inside the parentheses with the term outside. This can be done as follows:

$$-4(-2x + 7w) = -4(-2x) + (-4)(7w)$$

Using the distributive property, we can rewrite the expression as:

$$-4(-2x + 7w) = 8x - 28w$$

Combining Like Terms

Now that we have simplified the expression $-4(-2x + 7w)$, we can combine it with the other terms in the original expression. The original expression is:

$$-6w - 4(-2x + 7w) + 3x$$

Substituting the simplified expression $8x - 28w$ into the original expression, we get:

$$-6w + 8x - 28w + 3x$$

Simplifying the Expression

Now that we have combined all the like terms, we can simplify the expression further by combining the like terms. The expression can be rewritten as:

$$-6w - 28w + 8x + 3x$$

Combining the like terms, we get:

$$-34w + 11x$$

Conclusion

In this article, we simplified the given algebraic expression using the distributive property and combining like terms. We started by applying the distributive property to simplify the expression $-4(-2x + 7w)$, and then combined the like terms to simplify the original expression. The final simplified expression is $-34w + 11x$. This example demonstrates the importance of simplifying algebraic expressions in mathematics and how it can be achieved using the distributive property and combining like terms.

Tips and Tricks for Simplifying Algebraic Expressions

• Always start by applying the distributive property to simplify expressions with parentheses.
• Combine like terms by adding or subtracting the coefficients of the same variables.
• Use the distributive property to simplify expressions with multiple terms inside the parentheses.
• Simplify expressions by eliminating any unnecessary components, such as zero terms or terms that cancel each other out.

Common Mistakes to Avoid When Simplifying Algebraic Expressions

• Failing to apply the distributive property when simplifying expressions with parentheses.
• Not combining like terms, which can lead to incorrect simplifications.
• Simplifying expressions by eliminating necessary components, such as terms that are essential to the expression.
• Not checking the expression for any errors or inconsistencies after simplifying.

Real-World Applications of Simplifying Algebraic Expressions

Simplifying algebraic expressions has numerous real-world applications in various fields, including:

• Physics: Simplifying algebraic expressions is essential in physics to describe the motion of objects and the behavior of physical systems.
• Engineering: Simplifying algebraic expressions is crucial in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
• Computer Science: Simplifying algebraic expressions is essential in computer science to optimize algorithms and data structures.
• Economics: Simplifying algebraic expressions is crucial in economics to model and analyze economic systems and make predictions about future trends.

Final Thoughts

Simplifying algebraic expressions is a fundamental skill in mathematics that has numerous real-world applications. By applying the distributive property and combining like terms, we can simplify complex expressions and make them more manageable and easier to work with. In this article, we demonstrated how to simplify a given algebraic expression using the distributive property and combining like terms. We also provided tips and tricks for simplifying algebraic expressions and common mistakes to avoid.

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Introduction to Simplifying Algebraic Expressions Q&A

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

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand and simplify expressions by multiplying each term inside the parentheses with the term outside.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside. For example, if you have an expression like $-4(-2x + 7w)$, you would multiply $-4$ with each term inside the parentheses: $-4(-2x) + (-4)(7w)$.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) with the same exponent(s). For example, $2x$ and $5x$ are like terms because they both have the variable $x$ with an exponent of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the same variables. For example, if you have an expression like $3x + 2x$, you would combine the like terms by adding the coefficients: $3x + 2x = 5x$.

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

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

• Failing to apply the distributive property when simplifying expressions with parentheses.
• Not combining like terms, which can lead to incorrect simplifications.
• Simplifying expressions by eliminating necessary components, such as terms that are essential to the expression.
• Not checking the expression for any errors or inconsistencies after simplifying.

Q: How do I check my work when simplifying algebraic expressions?

A: To check your work when simplifying algebraic expressions, you should:

• Read the expression carefully to make sure you understand what it says.
• Apply the distributive property and combine like terms as needed.
• Check the expression for any errors or inconsistencies.
• Simplify the expression as much as possible.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has numerous real-world applications in various fields, including:

• Physics: Simplifying algebraic expressions is essential in physics to describe the motion of objects and the behavior of physical systems.
• Engineering: Simplifying algebraic expressions is crucial in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
• Computer Science: Simplifying algebraic expressions is essential in computer science to optimize algorithms and data structures.
• Economics: Simplifying algebraic expressions is crucial in economics to model and analyze economic systems and make predictions about future trends.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by:

• Working through practice problems in your textbook or online resources.
• Creating your own practice problems and simplifying them.
• Joining a study group or working with a tutor to practice simplifying algebraic expressions.

Conclusion

Simplifying algebraic expressions is a fundamental skill in mathematics that has numerous real-world applications. By applying the distributive property and combining like terms, we can simplify complex expressions and make them more manageable and easier to work with. In this article, we answered some frequently asked questions about simplifying algebraic expressions and provided tips and tricks for simplifying algebraic expressions.

Additional Resources

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

Final Thoughts

Simplifying algebraic expressions is a crucial skill in mathematics that has numerous real-world applications. By practicing simplifying algebraic expressions and applying the distributive property and combining like terms, you can become proficient in simplifying complex expressions and make them more manageable and easier to work with.