To solve the equation described, you would first set it up as follows:
\[ \frac{3}{4}x - 5 = 7 \]
Then, to isolate \(x\), you would first add 5 to both sides, which involves the Addition Property of Equality:
\[ \frac{3}{4}x = 12 \]
Next, to eliminate the fraction, you would multiply both sides by \(\frac{4}{3}\), which would involve the Multiplication Property of Equality.
However, since the question asks specifically for the last property of equality used, it would be the step where you multiplied through to isolate \(x\). Since that is not listed in the options, we can only rely on properties provided.
Thus, the last property specifically could refer to one of the changes made, and looking at the given choices, recognizing that you have just moved to the step involving multiplication:
The last property you would use for this context (as to why the equation is balanced) when applying the multiplication step is not listed, but would be aligned with the Multiplication Property of Equality if it was an available option.
So, if strictly using the options provided, the best selection would actually be Addition Property of Equality, as initially, you need to deal with balancing the subtraction of 5 to both sides, even though the predominant step thereafter involves multiplication.
But understand, after solving, if the problem focuses on balancing throughout, the option leading towards solving for \(x\) reflects prior changes effectively; hence, it diverges closer toward Multiplication Property of Equality but noting we end on the Addition Property of Equality as justified first stepping throughout consistently to maintain the original solution method.
Thus, selecting:
Addition Property of Equality
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