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.

Answer 1

Let's denote the original equation as \( x \).

1. **Starting with the original equation**: We will call it \( x = A \), where \( A \) is the expression we will solve.
2. **Subtract 5 from both sides**:
\[
x - 5 = A - 5
\]
3. **Multiply both sides by -2**:
\[
-2(x - 5) = -2(A - 5)
\]

Now, we need to isolate \( x \) in such a way that the final result gives \( x = 8 \).

### Solving for the original equation:

Given that the final answer is \( x = 8 \), we set up the equation.
1. **Starting from the final equation** \( x = 8 \):
\[
-2(x - 5) = -2(8 - 5) \\
-2(x - 5) = -2(3) \\
-2(x - 5) = -6
\]

2. **Divide both sides by -2**:
\[
x - 5 = 3
\]

3. **Add 5 to both sides**:
\[
x = 3 + 5 \\
x = 8
\]

This confirms that the original equation before the modifications was:
\[
x - 5 = 3
\]

Thus, if we rewrite:
- Original equation before these operations:
\[
x = 3 + 5 \implies x = 8
\]

Confirming the transformations:
1. **Subtracting 5**:
\[
x - 5 = 3
\]
2. **Multiplying through by -2**:
\[
-2(x - 5) = -6 \implies -2x + 10 = -6 \implies -2x = -16 \implies x = 8
\]

### Final Answer:

The original equation was:
\[
x - 5 = 3
\]
This correctly leads us to the final answer \( x = 8 \) when following the given instructions.