Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?

Question

A. Subtraction Property of Equality
B. Division Property of Equality
C. Addition Property of Equality
D. Identity Property of Multiplication

Answer 1

To solve the equation "Five less than three-fourths of x is seven," we first set up the equation:

\[ \frac{3}{4}x - 5 = 7 \]

To isolate \(\frac{3}{4}x\), we would first add 5 to both sides of the equation. This step utilizes the Addition Property of Equality.

\[ \frac{3}{4}x = 7 + 5 \] \[ \frac{3}{4}x = 12 \]

Next, to solve for \(x\), we would multiply both sides by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\). This step uses the Division Property of Equality, since multiplying by the reciprocal is essentially dividing by the fraction.

\[ x = 12 \cdot \frac{4}{3} \]

After simplifying that, we can calculate \(x\):

\[ x = 16 \]

In this context, since the final step was to isolate \(x\) by multiplying by \(\frac{4}{3}\), the last property of equality employed in this process was actually the Division Property of Equality.

Therefore, the answer is:

B. Division Property of Equality

Answer 2

are you sure this is correct

Answer 3

Let's revisit the problem step-by-step to ensure clarity and correctness.

We start with the equation:

\[ \frac{3}{4}x - 5 = 7 \]

Next, we add 5 to both sides to isolate the term with \(x\):

\[ \frac{3}{4}x - 5 + 5 = 7 + 5 \]

This simplifies to:

\[ \frac{3}{4}x = 12 \]

Now, to solve for \(x\), we multiply both sides by the reciprocal of \(\frac{3}{4}\):

\[ x = 12 \cdot \frac{4}{3} \]

This operation essentially involves using the multiplication property, but because we are isolating \(x\) we can also conceptualize it as dividing both sides by \(\frac{3}{4}\), which is the same as multiplying by \(\frac{4}{3}\).

The last property that directly allows us to find \(x\) (from \(\frac{3}{4}x = 12\) to solve for \(x\)) is indeed based on the operation performed at that point.

To clarify:

1. Addition Property of Equality is used first when we added 5 to both sides.
2. Division Property of Equality is then applied when we isolate \(x\).

Thus, the last property we used to arrive at the final value of \(x\) is the Division Property of Equality.

So yes, the original assessment that the answer is:

B. Division Property of Equality

is indeed correct. Thank you for prompting the review!