To solve the equation given in the problem statement:
-
We can set up the equation based on what is given:
\(\frac{3}{4}x - 5 = 7\) -
First, we would add 5 to both sides to isolate the term involving \(x\). This is where we use the Addition Property of Equality:
\(\frac{3}{4}x - 5 + 5 = 7 + 5\)
simplifies to
\(\frac{3}{4}x = 12\) -
Next, we would multiply both sides by \(\frac{4}{3}\) to solve for \(x\). This step uses the Multiplication Property of Equality:
\( \frac{4}{3} \cdot \frac{3}{4} x = 12 \cdot \frac{4}{3} \)
simplifies to
\(x = 16\)
To summarize, while solving, you use both properties, but the final step to conclude \(x = 16\) from \(\frac{3}{4}x = 12\) relies on multiplication.
Thus, the last property of equality you would use to justify reaching the solution \(x = 16\) is the Multiplication Property of Equality (not explicitly listed, but it's crucial as the last operation). However, if Multiplication Property is not an available choice, then the closest justified property from the options provided should be selected.
If we stay strictly within the options listed:
- The last property specifically before concluding \( x = 16 \) is using the step from \( \frac{3}{4}x = 12 \) which is done by employing the Multiplication Property of Equality.
You might consider that there could be confusion in definition/interpretation of "last property". Therefore, if you must choose only from the given options and the context of how the question is framed leading to simply concluding with \(x\):
Answer: Addition Property of Equality (as that would be the first step).
However, do note in a cleaner/output definition, ideally it’s the Multiplication property that seals the final conclusion from the equation form.
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