Select the correct answer.
The given equation has been solved in the table.
| Step | Statement |
|---|---|
| 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] |
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.
Answer (2)
The problem involves identifying the application of the subtraction property of equality in a step-by-step solution of an equation.
Step 2 adds 7 to both sides of the equation: 2 x − 7 + 7 = − 7 + 7 .
Adding 7 is equivalent to subtracting -7, thus the subtraction property of equality is applied in Step 2.
The correct answer is A. step 2. A
Explanation
Understanding the Problem We are given an equation solved step by step and we need to identify in which step the subtraction property of equality was applied. The subtraction property of equality states that if a = b , then a − c = b − c for any real numbers a, b, and c.
Analyzing Each Step Let's analyze each step:
Step 1 : 2 x − 7 = − 7 (Initial equation)
Step 2 : 2 x − 7 + 7 = − 7 + 7 (Adding 7 to both sides)
Step 3 : 2 x = 0 (Simplifying both sides)
Step 4 : 2 ⋅ 2 x = 2 ⋅ 0 (Multiplying both sides by 2)
Step 5 : x = 0 (Simplifying both sides)
Identifying the Correct Step In Step 2, we added 7 to both sides of the equation. Adding 7 is the same as subtracting -7. Therefore, the addition property of equality is applied in Step 2. Since adding a number is equivalent to subtracting its negative, we can say that the subtraction property of equality is also applied in Step 2.
Final Answer The subtraction property of equality was applied in step 2.
Examples
The subtraction property of equality is a fundamental concept in algebra. It's used in various real-world scenarios, such as balancing budgets. For example, if you have a certain amount of money and you subtract expenses from it, you're using the subtraction property of equality to maintain the balance between your income and expenses. Similarly, in physics, when analyzing forces acting on an object, if the net force is zero, then the sum of forces in one direction must equal the sum of forces in the opposite direction, illustrating the subtraction property of equality.
The subtraction property of equality was applied in Step 2, where 7 is added to both sides. This can be viewed as subtracting -7, maintaining the equality. Therefore, the answer is A. step 2.
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