Question

Identify the equation that is solved correctly given the following written directions: subtract 5 from both sides of the equation. Then, multiply both sides of the equation by negative 2. The final answer is x = 8.
A. x/-2 - 5 = 1
B. x/2 + 5 = 1
C. x/-2 + 5 = 1
D. x/2 - 5 = 1

Answer 1

Let's analyze the directions and find which equation leads to the final solution \( x = 8 \).

1. Start with the equation \( x = ? \) (we'll derive it from each option).
2. First, **subtract 5 from both sides**.
3. Then, **multiply both sides by -2**.

After these operations, we want to reach \( x = 8 \).

Let's go through each option:

### Option A: \( \frac{x}{-2} - 5 = 1 \)
1. Subtract 5 from both sides:
\[
\frac{x}{-2} = 1 + 5 = 6
\]
2. Multiply both sides by -2:
\[
x = 6 \times -2 = -12
\]

### Option B: \( \frac{x}{2} + 5 = 1 \)
1. Subtract 5 from both sides:
\[
\frac{x}{2} = 1 - 5 = -4
\]
2. Multiply both sides by -2:
\[
x = -4 \times -2 = 8
\]

### Option C: \( \frac{x}{-2} + 5 = 1 \)
1. Subtract 5 from both sides:
\[
\frac{x}{-2} = 1 - 5 = -4
\]
2. Multiply both sides by -2:
\[
x = -4 \times -2 = 8
\]

### Option D: \( \frac{x}{2} - 5 = 1 \)
1. Subtract 5 from both sides:
\[
\frac{x}{2} = 1 + 5 = 6
\]
2. Multiply both sides by -2:
\[
x = 6 \times -2 = -12
\]

After going through all options, we see that both **Option B** and **Option C** yield \( x = 8 \) after performing the operations. However, only one of these conforms to the original equation formats given:

1. **Option B** results in \( x = 8 \).
2. **Option C** also results in \( x = 8 \).

Since more than one option leads to the final result, you may consider both acceptable, but if only one needs to be identified in the context of a straightforward solution:

The correct identification of the option that directly leads to \( x = 8 \) after correctly following the operations specified is:
**B. \( \frac{x}{2} + 5 = 1 \)** is the simplest one to follow and likely the intended solution if a single answer is needed.