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

Answer 1

To solve the equation "five less than three-fourths of x is seven," we can set it up as follows:

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

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

1. **Add 5 to both sides:**
\[
\frac{3}{4}x = 12
\]

Here, we used the **Addition Property of Equality**.

2. **Multiply both sides by \(\frac{4}{3}\):**
\[
x = 16
\]

Here, we used the **Division Property of Equality** (or, in this case, it's essentially multiplying both sides by the reciprocal of the coefficient of \(x\)).

If we follow the sequence and identify the last property used in that process, it would be the **Addition Property of Equality**, as we added 5 to both sides first before dividing.

So, the last property of equality used to justify the solution is the **Addition Property of Equality**.