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

To find the equation that correctly leads to the final answer \( x = 8 \) using the given steps, we can work backwards from the final answer through the described operations: multiplying by -2 after subtracting 5.

1. Starting with the final answer:
\[
x = 8
\]

2. The last step before \( x = 8 \) was multiplying by -2. Therefore, before this operation, the equation was:
\[
-2 \cdot (x) = -16 \quad (\text{since } 8 \cdot -2 = -16)
\]
This implies:
\[
x = \frac{-16}{-2} = 8
\]

3. The expression before multiplying by -2 involved subtracting 5 from both sides, so:
\[
\text{Before multiplying: } x - 5 = -16
\]
Adding 5 to both sides gives:
\[
x = -16 + 5 = -11
\]

Now we need to find an equation among the options provided that can eventually lead through these steps to the solution of \( x = 8 \).

Let's manipulate each option to check their validity:

A) \( \frac{x}{-2} + 5 = 1 \)
\[
\frac{x}{-2} = 1 - 5 \implies \frac{x}{-2} = -4 \implies x = 8 \text{ (Correct after these steps)}
\]

B) \( \frac{x}{2} + 5 = 1 \)
\[
\frac{x}{2} = 1 - 5 \implies \frac{x}{2} = -4 \implies x = -8 \text{ (Incorrect)}
\]

C) \( \frac{x}{-2} - 5 = 1 \)
\[
\frac{x}{-2} = 1 + 5 \implies \frac{x}{-2} = 6 \implies x = -12 \text{ (Incorrect)}
\]

D) \( \frac{x}{2} - 5 = 1 \)
\[
\frac{x}{2} = 1 + 5 \implies \frac{x}{2} = 6 \implies x = 12 \text{ (Incorrect)}
\]

From the above checks, we can see that option A leads to \( x = 8 \) correctly, affirming the processes described in the question.

Thus, the correct answer is:
**A) \(\frac{x}{-2} + 5 = 1\)**.