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?
\\(\circ\\) a. step 2
\\(\circ\\) b. step 3
\\(\circ\\) c. step 4
\\(\circ\\) d. the subtraction property of equality was not applied to solve this equation.

Explanation:

Step1: Recall the properties of equality

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true. The addition property of equality is adding the same number to both sides. The multiplication property is multiplying both sides by the same non - zero number.

Step2: Analyze each step

• Step 2: In step 2, we have \(\frac{x}{2}-7 + 7=-7 + 7\). Here, we are adding 7 to both sides of the equation \(\frac{x}{2}-7=-7\) (from step 1). This is the addition property of equality, not the subtraction property.
• Step 3: \(\frac{x}{2}=0\) is the result of simplifying the left - hand side (\(-7 + 7 = 0\) and \(\frac{x}{2}-7 + 7=\frac{x}{2}\)) and the right - hand side (\(-7 + 7 = 0\)) of the equation in step 2. It is not an application of the subtraction property.
• Step 4: \(2\cdot\frac{x}{2}=2\cdot0\) is the multiplication property of equality (multiplying both sides by 2) to solve for \(x\).
• Since step 2 uses addition property, step 3 is simplification, step 4 uses multiplication property, the subtraction property of equality was not applied in any of the steps to solve this equation.

Answer:

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