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?

Answer 1

To solve the problem, we can set up the equation based on the statement "Five less than three-fourths of x is seven." This can be written mathematically as:

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

Now, we can solve for \( x \) step by step:

1. Add 5 to both sides to isolate the term with \( x \): \[ \frac{3}{4}x - 5 + 5 = 7 + 5 \] Simplifying this gives: \[ \frac{3}{4}x = 12 \]

2. Next, multiply both sides by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \): \[ x = 12 \cdot \frac{4}{3} \] This simplifies to: \[ x = 16 \]

Now, since \( x = 16 \) is given, we confirm this is the solution.

In reasoning through what would be the last property of equality used to justify the solution to this equation, we see that the final step was multiplying both sides of the equation by \( \frac{4}{3} \). Thus, the last property of equality used in the context of solving this equation is the Multiplication Property of Equality, which states that if two quantities are equal, you can multiply both sides by the same non-zero number and the equation will remain true.

So, the last property of equality you would use to justify the solution is:

Multiplication Property of Equality.