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Understanding the Distributive Property with (7 - 4n) • 6
The distributive property is a fundamental concept in algebra that allows us to simplify expressions involving multiplication and addition/subtraction. It states that multiplying a sum by a number is the same as multiplying each term of the sum by that number individually, then adding the products.
Let's apply this to the expression (7 - 4n) • 6.
Applying the Distributive Property
- Identify the terms inside the parentheses: In this case, we have 7 and -4n.
- Multiply each term by the number outside the parentheses: This means multiplying both 7 and -4n by 6.
- 7 • 6 = 42
- (-4n) • 6 = -24n
- Combine the results: Since we were originally subtracting, we keep the subtraction sign between the terms.
Therefore, (7 - 4n) • 6 = 42 - 24n
Why is the Distributive Property Important?
The distributive property helps us simplify expressions and solve equations. By breaking down complex expressions into simpler ones, we can:
- Solve for unknown variables: Applying the distributive property allows us to isolate variables and solve equations.
- Evaluate expressions: We can efficiently calculate the value of expressions with multiple operations.
- Simplify complex equations: By distributing multiplication, we can create equations that are easier to work with.
Example: Solving an Equation using the Distributive Property
Let's say we have the equation: 2(x + 3) = 10
- Apply the distributive property: 2(x + 3) becomes 2x + 6
- Now the equation is: 2x + 6 = 10
- Solve for x:
- Subtract 6 from both sides: 2x = 4
- Divide both sides by 2: x = 2
The distributive property allows us to solve for x in a systematic and efficient way.
Conclusion
The distributive property is a powerful tool in algebra that simplifies expressions and helps us solve equations. Understanding and applying this property is crucial for success in various mathematical concepts and problem-solving.