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 (1)
The problem requires identifying the step where the subtraction property of equality is applied in solving the equation 2 x − 7 = − 7 . The addition property of equality is applied in step 2. Since the subtraction property of equality was not directly applied, the answer is D. The subtraction property of equality was not applied to solve this equation.
Explanation
Understanding the Problem We are given an equation solved step-by-step in a table and asked to identify the step where 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 number c . However, in this problem, we are looking for the application of the addition property of equality, which states that if a = b , then a + c = b + c for any real number c .
Analyzing Each Step Let's examine each step:
Step 1: 2 x − 7 = − 7
Step 2: 2 x − 7 + 7 = − 7 + 7 . Here, we add 7 to both sides of the equation.
Step 3: 2 x = 0
Step 4: 2 ⋅ 2 x = 2 ⋅ 0 . Here, we multiply both sides of the equation by 2.
Step 5: x = 0
Identifying the Correct Step In step 2, we added 7 to both sides of the equation: 2 x − 7 + 7 = − 7 + 7 . This is an application of the addition property of equality. The question, however, asks about the subtraction property of equality. Since adding 7 is equivalent to subtracting -7, we can say that the addition property of equality was applied in step 2. However, the question explicitly asks for the subtraction property. Looking at the steps, we see that the addition property was applied, but the subtraction property was not directly applied.
Final Answer Therefore, the correct answer is that the subtraction property of equality was not applied to solve this equation.
Examples
The properties of equality, such as the addition and subtraction properties, are fundamental in solving algebraic equations. For instance, if you're balancing a budget and need to adjust expenses to match your income, these properties help ensure that the equation (budget) remains balanced. Similarly, in physics, when calculating forces acting on an object, these properties ensure that the net force equation remains valid as you manipulate terms to solve for unknowns. These principles are not just theoretical; they're essential tools for maintaining balance and accuracy in various real-world calculations.
