Linear Equations in Real-World Scenarios Quick Check

Question

3 of 53 of 5 Items
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

Identity Property of Multiplication
Identity Property of Multiplication

Division Property of Equality
Division Property of Equality

Addition Property of Equality
Addition Property of Equality

Subtraction Property of Equality

Answer 1

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

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

To isolate \(x\), we would add 5 to both sides first:

\[ \frac{3}{4}x = 12 \]

Next, we would multiply both sides by \( \frac{4}{3} \) to solve for \(x\):

\[ x = 12 \cdot \frac{4}{3} \]

At this last step, we used the Identity Property of Multiplication.

Thus, the last property of equality used to justify the solution would be the Identity Property of Multiplication.