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 solve each option step-by-step according to the given instructions: subtract 5 from both sides, then multiply by -2 to see which one leads to the final answer \( x = 8 \).

1. **Option A: \( \frac{x}{-2} + 5 = 1 \)**

- **Subtract 5 from both sides:**
\[
\frac{x}{-2} = 1 - 5 \\
\frac{x}{-2} = -4
\]

- **Multiply both sides by -2:**
\[
x = -2 \times -4 \\
x = 8
\]

**This option works.**

2. **Option B: \( \frac{x}{2} + 5 = 1 \)**

- **Subtract 5 from both sides:**
\[
\frac{x}{2} = 1 - 5 \\
\frac{x}{2} = -4
\]

- **Multiply both sides by -2:**
\[
x = -2 \times -4 \\
x = 8
\]

**This option works.**

3. **Option C: \( \frac{x}{-2} - 5 = 1 \)**

- **Subtract -5 (which is equivalent to adding 5) from both sides:**
\[
\frac{x}{-2} = 1 + 5 \\
\frac{x}{-2} = 6
\]

- **Multiply both sides by -2:**
\[
x = -2 \times 6 \\
x = -12
\]

**This option does NOT work.**

4. **Option D: \( \frac{x}{2} - 5 = 1 \)**

- **Subtract -5 (which is equivalent to adding 5) from both sides:**
\[
\frac{x}{2} = 1 + 5 \\
\frac{x}{2} = 6
\]

- **Multiply both sides by -2:**
\[
x = -2 \times 6 \\
x = -12
\]

**This option does NOT work.**

Thus, both **Option A** and **Option B** lead to the final answer \( x = 8 \).