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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?(

3 answers

To solve the problem, we start with the equation that represents the given situation:

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

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

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

  2. Multiply both sides by \( \frac{4}{3} \) to isolate \( x \): \[ x = 12 \times \frac{4}{3} \] This simplifies to: \[ x = 16 \]

Now, you're tasked with identifying the last property of equality used in the solution:

The last operation we performed was multiplying both sides of the equation by \( \frac{4}{3} \) to isolate \( x \). Therefore, the last property of equality we used is the Multiplication Property of Equality, which states that if two expressions are equal, multiplying both sides by the same non-zero number will keep the expressions equal.

So, the last property of equality you would use to justify the solution to this problem is the Multiplication Property of Equality.

Answer Choice:

Identity Property of Multiplication
Identity Property of Multiplication

Subtraction Property of Equality
Subtraction Property of Equality

Division Property of Equality
Division Property of Equality

Addition Property of Equality

Given the choices provided, let's clarify the relevant steps we took in solving the equation:

  1. We started with the equation: \[ \frac{3}{4}x - 5 = 7 \]

  2. We added 5 to both sides, which involves the Addition Property of Equality: \[ \frac{3}{4}x = 12 \]

  3. Then, we multiplied both sides by \( \frac{4}{3} \), which involves the Multiplication Property of Equality.

Based on your choices, the last operation we performed—and the property that corresponds to the last step—was multiplication, which isn't listed in your options. However, since we want to justify each action taken:

  • The first action was adding 5 (Addition Property of Equality).
  • The second action was multiplying (Multiplication Property of Equality).

Among the choices you provided, since we performed addition before the last step, the closest relevant option that describes an operation we did is:

Addition Property of Equality.

However, if the answer explicitly requires the final justification for the last step, you may want to note that the last action before concluding was multiplication, but that option isn't listed. Therefore, in terms of the sequence of justification and choices presented, "Addition Property of Equality" is the best fit from the provided options.