## 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.