Which expression is equivalent to 6(x-4)

Which expression is equivalent to 6(x-4)?
O-6x + 4
6x-4
O6x-24
O-6x + 24

The Correct Answer and Explanation is :

To determine which expression is equivalent to (6(x – 4)), we can apply the distributive property, which states that (a(b + c) = ab + ac). In this case, we can treat (6) as (a) and (x – 4) as (b + c).

Step-by-Step Solution

1. Identify the Expression:
   [
   6(x – 4)
   ]
2. Apply the Distributive Property:
   [
   6(x – 4) = 6 \cdot x + 6 \cdot (-4)
   ]
3. Calculate Each Term:

• The first term: (6 \cdot x = 6x)
• The second term: (6 \cdot (-4) = -24)

1. Combine the Terms:
   [
   6x – 24
   ]

Conclusion

The expression (6(x – 4)) simplifies to (6x – 24).

Evaluate the Options

Now, let’s compare this with the given options:

1. (-6x + 4)
2. (6x – 4)
3. (6x – 24) (Correct Answer)
4. (-6x + 24)

The correct answer is (6x – 24).

Explanation of Other Options

• Option 1: (-6x + 4): This expression is not equivalent because it represents a different linear equation. The coefficients and constants do not match our derived expression.
• Option 2: (6x – 4): While it shares the (6x) term, the constant (-4) differs from (-24), so it cannot be equivalent.
• Option 4: (-6x + 24): This is also not equivalent, as it has a negative coefficient for (x) and a positive constant, diverging from the correct result.

Summary

Thus, through the application of the distributive property, we find that the equivalent expression to (6(x – 4)) is indeed (6x – 24). This reinforces the importance of understanding how to manipulate algebraic expressions correctly.