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?(1 point) Responses Identity Property of Multiplication Identity Property of Multiplication Division Property of Equality Division Property of Equality Addition Property of Equality Addition Property of Equality Subtraction Property of Equality

To solve the equation "Five less than three-fourths of x is seven," we can express it mathematically as:

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

If we substitute \( x = 16 \) into the equation, we get:

\[
\frac{3}{4}(16) - 5 = 7
\]

Calculating \( \frac{3}{4}(16) \):

\[
\frac{3 \times 16}{4} = \frac{48}{4} = 12
\]

Now, substituting back into the equation:

\[
12 - 5 = 7
\]

This holds true, confirming that \( x = 16 \) is indeed a solution.

To derive the equation from the original statement, we would have performed the following steps:

1. **Add 5 to both sides** of the equation to isolate the term with \( x \):
\[
\frac{3}{4}x = 7 + 5
\]

2. This results in:
\[
\frac{3}{4}x = 12
\]

3. **Multiply both sides by the reciprocal** of \( \frac{3}{4} \), which is \( \frac{4}{3} \), to solve for \( x \).

Thus, the last property of equality used in the justification for the solution would be:

**Multiplication Property of Equality** (specifically multiplying both sides by \( \frac{4}{3} \)).

However, since the options provided indicate "Identity Property of Multiplication," "Addition Property of Equality," and "Subtraction Property of Equality" without directly mentioning multiplication's reciprocal, the closest answer that refers to the final step of solving for \( x \) would be the **Multiplication Property of Equality** if it were an option.

If we consider only the provided options, after isolating terms, the answer could be pointed to **Addition Property of Equality** as it involves adding numbers to both sides as a step towards the final simplification.