Question

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

Division Property of Equality
Division Property of Equality

Subtraction Property of Equality
Subtraction Property of Equality

Addition Property of Equality
Addition Property of Equality

Identity Property of Multiplication

Answer 1

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

\(\frac{3}{4}x - 5 = 7\)

To isolate \(x\), we can follow these steps:

1. **Add 5** to both sides to eliminate the -5 from the left side:

\(\frac{3}{4}x - 5 + 5 = 7 + 5\)

This simplifies to:

\(\frac{3}{4}x = 12\)

2. Next, to eliminate the fraction, we **multiply** both sides by \(\frac{4}{3}\):

\(\frac{4}{3} \cdot \frac{3}{4} x = 12 \cdot \frac{4}{3}\)

This simplifies to:

\(x = 16\)

In this set of operations, we first used the **Addition Property of Equality** when we added 5 to both sides of the equation.

Therefore, the last property of equality you would use to justify the solution to this problem is the **Division Property of Equality** when you multiplied both sides by \(\frac{4}{3}\).

So, the correct answer is:

**Division Property of Equality**.