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 Subtraction Property of Equality Subtraction Property of Equality Division Property of Equality Division Property of Equality Addition Property of Equality Addition Property of Equality Identity Property of Multiplication

Answer 1

To solve the equation based on the problem statement "Five less than three-fourths of x is seven," we first express this mathematically:

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

Next, we can solve this equation step-by-step:

1. Add 5 to both sides to eliminate the -5: \[ \frac{3}{4}x = 7 + 5 \] \[ \frac{3}{4}x = 12 \]

2. Multiply both sides by the reciprocal of \(\frac{3}{4}\) (which is \(\frac{4}{3}\)) to isolate \(x\): \[ x = 12 \times \frac{4}{3} \]

3. Calculate the right side: \[ x = 16 \]

In this process, the last property of equality utilized was the Multiplication Property of Equality, because that was the final step to isolate \(x\).

So the answer is:

Identity Property of Multiplication.