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.(1 point)
Responses

x−2+5=1
x over negative 2 plus 5 is equal to 1

x2−5=1
x over 2 minus 5 is equal to 1

x−2−5=1
x over negative 2 minus 5 is equal to 1

x2+5=1

Answer 1

To determine which equation is solved correctly given the instructions, we can follow the directions step by step on each response.

### Directions:
1. **Subtract 5 from both sides.**
2. **Multiply both sides by -2.**
3. **The final answer is x = 8.**

We'll evaluate each equation based on these directions:

1. **For \( x - 2 + 5 = 1 \):**
- Simplifying: \( x + 3 = 1 \)
- Subtracting 5: \( x + 3 - 5 = 1 - 5 \) → \( x - 2 = -4 \)
- Multiplying both sides by -2: \( -2(x - 2) = -2(-4) \) → \( -2x + 4 = 8 \)
- Rearranging gives \( -2x = 4 \) → \( x = -2 \) (not correct)

2. **For \( \frac{x}{-2} + 5 = 1 \):**
- Subtracting 5: \( \frac{x}{-2} = 1 - 5 \) → \( \frac{x}{-2} = -4 \)
- Multiplying by -2: \( x = -4 \times -2 \) → \( x = 8 \) (correct)

3. **For \( x - 2 - 5 = 1 \):**
- Simplifying: \( x - 7 = 1 \)
- Subtracting 5: \( x - 7 - 5 = 1 - 5 \) → \( x - 7 = -4 \)
- Multiplying both sides by -2: \( -2(x - 7) = -2(-4) \) → \( -2x + 14 = 8 \)
- Rearranging gives \( -2x = -6 \) → \( x = 3 \) (not correct)

4. **For \( x^2 + 5 = 1 \):**
- Subtracting 5: \( x^2 = 1 - 5 \) → \( x^2 = -4 \) (not a valid real solution)

### Conclusion:
The equation that leads to \( x = 8 \) after following the directions is:

**\(\frac{x}{-2} + 5 = 1\)**