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.

Question

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 \( x = 8 \).