Final answer:
The correct choice is D, because 5(x-6) simplifies to 5x - 30, which is not equal to 5x - 65, making the equation inconsistent and therefore the statement false.
Step-by-step explanation:
The correct answer is option D, because the equation is inconsistent. To evaluate whether 5(x-6) equals 5x - 65 is a true statement or not, we distribute the 5 on the left-hand side which gives us 5x - 30. Now, we compare this with the right-hand side of the equation, 5x - 65.
To determine if the given equation is true or false, we need to simplify both sides and see if they are equal.
Let's simplify the left-hand side of the equation:
5(x-6) = 5x - 30
And now the right-hand side:
5x - 65
As we can see, the simplified form of both sides is not equal. Therefore, the equation is false.
When we look at both sides, it is evident that -30 does not equal -65. This means the equation is not balanced, leading to inconsistency. Since the equation does not hold true, options A and B can be dismissed as they imply the equation is correct. Additionally, option C is not true because the coefficients, which are the numbers in front of x (both 5), are indeed equal on both sides.