In solving the equation [tex]\(\frac{x}{2}-7=-7\)[/tex], we need to carefully examine each step to identify when the subtraction property of equality was applied.
Here is the given sequence of steps:
1. [tex]\(\frac{x}{2}-7=-7\)[/tex]
2. [tex]\(\frac{x}{2}-7+7=-7+7\)[/tex]
3. [tex]\(\frac{x}{2}=0\)[/tex]
4. [tex]\(2 \cdot \frac{x}{2}=2 \cdot 0\)[/tex]
5. [tex]\(x=0\)[/tex]
The subtraction property of equality states that if you subtract the same value from both sides of an equation, the resulting equation will still hold true. In this particular case:
- In Step 2, the equation [tex]\(\frac{x}{2}-7=-7\)[/tex] was modified by adding 7 to both sides, resulting in [tex]\(\frac{x}{2}-7+7=-7+7\)[/tex]. This step effectively cancels out the [tex]\(-7\)[/tex] on the left side of the equation:
[tex]\[\frac{x}{2}-7+7 = -7+7\][/tex]
Simplifies to:
[tex]\[\frac{x}{2} = 0\][/tex]
Thus, the operation performed in Step 2 is crucial because it involved the application of the rule allowing the addition of 7 to both sides, effectively using the concept that subtracting -7+7 is equivalent to zeroizing the constant on the left side.
Therefore, the subtraction property of equality was key in Step 2.
The correct answer is:
A. step 2
