Which of the following is equivalent to 12x +8?

Rationale

4(3x+2) is equivalent to 12x + 8.

By distributing the 4 in the expression 4(3x + 2), we obtain 12x + 8, confirming that this choice is equivalent to the original expression.

A (4(3x+2)) CORRECT

When we distribute 4 to both terms inside the parentheses, we get 4 * 3x + 4 * 2, which simplifies to 12x + 8. This shows that the expression is indeed equivalent to 12x + 8.

B (4(3x+8)) YOUR ANSWER

Distributing 4 in this expression gives us 4 * 3x + 4 * 8, which simplifies to 12x + 32. This is not equivalent to 12x + 8, as the constant term differs significantly.

C (4(3x+2x)) YOUR ANSWER

Here, distributing 4 leads to 4 * 3x + 4 * 2x, simplifying to 12x + 8x, which results in 20x. This is not equivalent to 12x + 8, as it represents a different expression altogether.

D (20x) YOUR ANSWER

This option presents a linear expression solely in terms of x. It does not include any constant term and is thus not equivalent to 12x + 8, which has both a variable and a constant component.

Conclusion

The only expression that correctly simplifies to 12x + 8 is 4(3x + 2). The other options either misrepresent the distribution of terms or yield entirely different expressions. Understanding how to distribute and combine like terms is key to identifying equivalent algebraic expressions.