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5(x-6) = 5x - 65. Is this a true statement? Why or why not?

A) True, because the coefficients on both sides are equal.
B) True, because the equation is balanced.
C) False, because the coefficients on both sides are not equal.
D) False, because the equation is inconsistent.

1 Answer

6 votes

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.

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