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/−2−5=1

x/2−5=1

x/2+5=1

Answer 1

which answer is most likely correct

Answer 2

To find the equation that leads to the solution \( x = 8 \) after following the given steps, let's analyze each option based on the provided instructions: subtract 5 from both sides, then multiply by -2.

1. For the equation \( \frac{x}{-2} + 5 = 1 \):
- Subtract 5 from both sides:
\[ \frac{x}{-2} = 1 - 5 \]
\[ \frac{x}{-2} = -4 \]
- Multiply by -2:
\[ x = 8 \] (This leads to the final answer.)

2. For the equation \( \frac{x}{-2} - 5 = 1 \):
- Subtract 5 from both sides:
\[ \frac{x}{-2} = 1 + 5 \]
\[ \frac{x}{-2} = 6 \]
- Multiply by -2:
\[ x = -12 \] (This does not lead to the final answer.)

3. For the equation \( \frac{x}{2} - 5 = 1 \):
- Subtract 5 from both sides:
\[ \frac{x}{2} = 1 + 5 \]
\[ \frac{x}{2} = 6 \]
- Multiply by -2:
\[ x = -12 \] (This also does not lead to the final answer.)

4. For the equation \( \frac{x}{2} + 5 = 1 \):
- Subtract 5 from both sides:
\[ \frac{x}{2} = 1 - 5 \]
\[ \frac{x}{2} = -4 \]
- Multiply by -2:
\[ x = 8 \] (This leads to the final answer as well.)

So based on this analysis, the equations \( \frac{x}{-2} + 5 = 1 \) and \( \frac{x}{2} + 5 = 1 \) both solve correctly to \( x = 8 \). However, the first and last equations represent valid scenarios under subtraction and multiplication, providing the same solution.

**Final Answer: x/−2+5=1** or **x/2+5=1**. Depending on your preference based on the directionality of \( x = 8 \), you may select either. If restricted to one answer option, choosing the first one explicitly states the manipulation process involving subtraction leading to a conclusion of \( x = 8 \).

Answer 3

The most correct answer based on the problem instructions is:

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

Here's the breakdown of how this leads to \( x = 8 \):

1. Start with the equation \( \frac{x}{-2} + 5 = 1 \).
2. Subtract 5 from both sides:
\[
\frac{x}{-2} = 1 - 5
\]
\[
\frac{x}{-2} = -4
\]
3. Multiply both sides by -2:
\[
x = -4 \cdot -2 = 8
\]

This matches the final answer of \( x = 8 \) as specified in your question.

The other option \( \frac{x}{2} + 5 = 1 \) also results in \( x = 8 \), but the instructions specifically mention subtracting 5 to manipulate an equation where \( x \) is divided by -2. Therefore, the best choice according to the given manipulation is \( \frac{x}{-2} + 5 = 1 \).