To solve the equation "Five less than three-fourths of x is seven," we can start by converting this into a mathematical expression.
This can be written as:
\[ \frac{3}{4}x - 5 = 7 \]
To isolate the term with \(x\), you would first need to add 5 to both sides of the equation:
\[ \frac{3}{4}x - 5 + 5 = 7 + 5 \]
This simplifies to:
\[ \frac{3}{4}x = 12 \]
Next, to solve for \(x\), you would multiply both sides of the equation by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\):
\[ x = 12 \cdot \frac{4}{3} \]
Now, we need to compute \(12 \cdot \frac{4}{3}\):
\[ x = 16 \]
If \(x = 16\), the last property of equality that we used to justify the solution is the Multiplication Property of Equality because we multiplied both sides of the equation by \(\frac{4}{3}\) to isolate \(x\).
Therefore, the correct response is:
Identity Property of Multiplication (which states that you can multiply both sides of an equation by the same non-zero number).
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