Simplify The Expression:${ 7(6 - 3g) = \square }$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems more efficiently. It involves rewriting complex expressions in a simpler form, making it easier to understand and work with. In this article, we will focus on simplifying the expression 7(6 - 3g) = ?. We will break down the steps involved in simplifying this expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is 7(6 - 3g) = ?. To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: Evaluate any exponents (none in this case).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is 6 - 3g. To evaluate this expression, we need to subtract 3g from 6.

# Evaluate the expression inside the parentheses
def evaluate_parentheses(g):
    return 6 - 3 * g

g = 1
print(evaluate_parentheses(g))  # Output: 3

Step 2: Multiply 7 by the Result

Now that we have evaluated the expression inside the parentheses, we can multiply 7 by the result.

# Multiply 7 by the result
def multiply_by_7(result):
    return 7 * result


result = 3
print(multiply_by_7(result))  # Output: 21

Step 3: Simplify the Expression

Now that we have multiplied 7 by the result, we can simplify the expression.

# Simplify the expression
def simplify_expression(g):
    result = 6 - 3 * g
    return 7 * result


g = 1
print(simplify_expression(g))  # Output: 21

Conclusion

In this article, we simplified the expression 7(6 - 3g) = ?. We followed the order of operations (PEMDAS) and broke down the steps involved in simplifying the expression. We evaluated the expression inside the parentheses, multiplied 7 by the result, and simplified the expression. The final simplified expression is 21.

Final Answer

The final answer is 21\boxed{21}.

Related Topics

  • Simplifying expressions
  • Order of operations (PEMDAS)
  • Algebraic expressions

Example Use Cases

  • Simplifying expressions in algebra
  • Evaluating expressions in calculus
  • Solving problems in physics and engineering

Tips and Tricks

  • Always follow the order of operations (PEMDAS)
  • Break down complex expressions into simpler ones
  • Use algebraic manipulations to simplify expressions

Common Mistakes

  • Failing to follow the order of operations (PEMDAS)
  • Not breaking down complex expressions into simpler ones
  • Not using algebraic manipulations to simplify expressions

Additional Resources

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

Introduction

In our previous article, we simplified the expression 7(6 - 3g) = ?. We followed the order of operations (PEMDAS) and broke down the steps involved in simplifying the expression. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate the expression inside the parentheses first.
  • Exponents: Evaluate any exponents (such as squaring or cubing) next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression with multiple operations?

A: To simplify an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Then, evaluate any exponents. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

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

A: Simplifying an expression involves rewriting it in a simpler form, often by combining like terms or canceling out common factors. Evaluating an expression, on the other hand, involves finding the value of the expression by substituting specific values for the variables.

Q: How do I simplify an expression with variables?

A: To simplify an expression with variables, follow the same steps as before. First, evaluate any expressions inside parentheses. Then, evaluate any exponents. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the final answer to the expression 7(6 - 3g) = ?

A: The final answer to the expression 7(6 - 3g) = is 21.

Q: Can I use a calculator to simplify expressions?

A: Yes, you can use a calculator to simplify expressions. However, it's always a good idea to check your work by hand to make sure you understand the steps involved in simplifying the expression.

Q: How do I know if an expression is simplified?

A: An expression is simplified when it can be rewritten in a simpler form, often by combining like terms or canceling out common factors. To check if an expression is simplified, try to rewrite it in a simpler form by combining like terms or canceling out common factors.

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions. We covered topics such as the order of operations (PEMDAS), simplifying and evaluating expressions, and working with variables. We also provided some tips and tricks for simplifying expressions.

Final Answer

The final answer is 21\boxed{21}.

Related Topics

  • Simplifying expressions
  • Order of operations (PEMDAS)
  • Algebraic expressions

Example Use Cases

  • Simplifying expressions in algebra
  • Evaluating expressions in calculus
  • Solving problems in physics and engineering

Tips and Tricks

  • Always follow the order of operations (PEMDAS)
  • Break down complex expressions into simpler ones
  • Use algebraic manipulations to simplify expressions

Common Mistakes

  • Failing to follow the order of operations (PEMDAS)
  • Not breaking down complex expressions into simpler ones
  • Not using algebraic manipulations to simplify expressions

Additional Resources

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