Simplify \[$ 7(A - 6) \$\].A. \[$ 7A - 42 \$\]B. \[$ A - 6 \$\]C. \[$ 7A - 6 \$\]

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Introduction

In mathematics, simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. One of the most common operations in algebra is the distributive property, which allows us to expand expressions inside parentheses. In this article, we will focus on simplifying the expression { 7(A - 6) $}$ using the distributive property.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that states:

a(b + c) = ab + ac

This property allows us to distribute a single term to multiple terms inside parentheses. In the expression { 7(A - 6) $}$, we have a single term 7 multiplied by a binomial expression (A - 6).

Step 1: Apply the Distributive Property

To simplify the expression { 7(A - 6) $}$, we will apply the distributive property by multiplying 7 to each term inside the parentheses.

7(A - 6) = 7A - 7(6)

Step 2: Simplify the Expression

Now, we will simplify the expression by evaluating the product of 7 and 6.

7A - 7(6) = 7A - 42

Conclusion

In conclusion, the simplified expression of { 7(A - 6) $}$ is { 7A - 42 $}$. This result is obtained by applying the distributive property and simplifying the expression.

Comparison with Other Options

Let's compare the simplified expression with the other options provided:

  • Option A: { 7A - 42 $}$: This is the correct simplified expression.
  • Option B: { A - 6 $}$: This option is incorrect because it does not apply the distributive property.
  • Option C: { 7A - 6 $}$: This option is also incorrect because it does not account for the product of 7 and 6.

Real-World Applications

Simplifying algebraic expressions like { 7(A - 6) $}$ has numerous real-world applications in fields such as:

  • Science: In physics, algebraic expressions are used to describe the motion of objects and the behavior of physical systems.
  • Engineering: In engineering, algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: In economics, algebraic expressions are used to model economic systems and make predictions about economic trends.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions like { 7(A - 6) $}$:

  • Apply the distributive property: This is the key to simplifying expressions with parentheses.
  • Simplify the expression: Once you have applied the distributive property, simplify the expression by evaluating products and combining like terms.
  • Check your work: Always check your work by plugging in values or using a calculator to verify the result.

Conclusion

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states:

a(b + c) = ab + ac

This property allows us to distribute a single term to multiple terms inside parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the single term to each term inside the parentheses. For example, in the expression { 7(A - 6) $}$, we would multiply 7 to each term inside the parentheses:

7(A - 6) = 7A - 7(6)

Q: What is the correct simplified expression of { 7(A - 6) $}$?

A: The correct simplified expression of { 7(A - 6) $}$ is { 7A - 42 $}$. This result is obtained by applying the distributive property and simplifying the expression.

Q: Why is it important to simplify algebraic expressions?

A: Simplifying algebraic expressions is important because it helps us to:

  • Understand the structure of the expression: By simplifying the expression, we can see the individual terms and their relationships.
  • Perform calculations more easily: Simplified expressions are often easier to work with and can make calculations more straightforward.
  • Make predictions and models: Simplified expressions can be used to make predictions and models in various fields, such as science, engineering, and economics.

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

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

  • Not applying the distributive property: Failing to apply the distributive property can lead to incorrect results.
  • Not simplifying the expression: Failing to simplify the expression can make it difficult to work with and understand.
  • Not checking work: Failing to check work can lead to errors and incorrect results.

Q: How can I practice simplifying algebraic expressions?

A: There are many ways to practice simplifying algebraic expressions, including:

  • Working through examples: Practice simplifying expressions by working through examples and exercises.
  • Using online resources: Utilize online resources, such as video tutorials and practice problems, to help you learn and practice simplifying expressions.
  • Seeking help: Don't be afraid to ask for help if you're struggling with simplifying expressions.

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

A: Simplifying algebraic expressions has numerous real-world applications in fields such as:

  • Science: In physics, algebraic expressions are used to describe the motion of objects and the behavior of physical systems.
  • Engineering: In engineering, algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: In economics, algebraic expressions are used to model economic systems and make predictions about economic trends.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill that has numerous real-world applications. By applying the distributive property and simplifying the expression, we can obtain the correct result. Remember to always check your work and use the tips and tricks provided to help you simplify expressions like this one.