Question

select the correct answer.
the given equation has been solved in the table.

step	statement
2	\\(\frac{x}{2} - 7 + 7 = -7 + 7\\)
3	\\(\frac{x}{2} = 0\\)
4	\\(2 \cdot \frac{x}{2} = 2 \cdot 0\\)
5	\\(x = 0\\)

in which step was the subtraction property of equality applied?
a. step 2
b. step 3
c. step 4
d. the subtraction property of equality was not applied to solve this equation.

Explanation:

Step1: Recall the subtraction property of equality

The subtraction property of equality states that if \(a = b\), then \(a - c = b - c\) for any real number \(c\). Similarly, the addition property of equality is if \(a = b\), then \(a + c = b + c\).

Step2: Analyze each step

• Step 2: \(\frac{x}{2}-7 + 7=-7 + 7\) uses the addition property of equality (adding 7 to both sides).
• Step 3: Is the result of simplifying step 2, no property of equality is applied here (just arithmetic simplification).
• Step 4: \(2\cdot\frac{x}{2}=2\cdot0\) uses the multiplication property of equality (multiplying both sides by 2).
• Now, check if subtraction property is applied: In step 2, we add 7, step 4 we multiply by 2. There is no step where we subtract a number from both sides. So the subtraction property of equality was not applied.

Answer:

D. The subtraction property of equality was not applied to solve this equation.