\((\mathrm{p} + 5) \times 2 = 8\)What value of p is the solution to the given equation?-1139

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{(p + 5) × 2 = 8}\)
  • Need to find the value of p that makes this equation true

2. SIMPLIFY by undoing operations in reverse order

• The equation shows: \(\mathrm{(p + 5)}\) is first, then multiplied by 2
• To isolate p, we need to undo these operations in reverse order
• First undo the multiplication by 2, then undo the addition of 5

3. SIMPLIFY step 1: Divide both sides by 2

• \(\mathrm{(p + 5) × 2 = 8}\)
• \(\mathrm{(p + 5) = 8 ÷ 2}\)
• \(\mathrm{(p + 5) = 4}\)

4. SIMPLIFY step 2: Subtract 5 from both sides

• \(\mathrm{p + 5 = 4}\)
• \(\mathrm{p = 4 - 5}\)
• \(\mathrm{p = -1}\)

5. Verify the solution

• Check: \(\mathrm{(-1 + 5) × 2 = 4 × 2 = 8}\) ✓

Answer: A) -1

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make sign errors when subtracting 5 from 4, incorrectly calculating \(\mathrm{4 - 5 = 1}\) instead of \(\mathrm{-1}\).

This computational mistake stems from confusion about subtracting a larger number from a smaller positive number. They may think "4 minus 5" gives a positive result because they focus on the digits rather than the direction on the number line.

This may lead them to select Choice B (1).

Second Most Common Error:

Poor SIMPLIFY sequencing: Students attempt to subtract 5 first before dividing by 2, incorrectly trying to distribute: \(\mathrm{(p + 5) × 2 = 8}\) becomes \(\mathrm{p + 5 × 2 = 8}\), then \(\mathrm{p + 10 = 8}\).

This order-of-operations confusion leads them to calculate \(\mathrm{p = 8 - 10 = -2}\), which isn't among the choices, causing confusion and potentially guessing.

The Bottom Line:

This problem tests whether students can systematically undo operations in the correct reverse order and handle arithmetic with negative results. The key insight is recognizing that \(\mathrm{4 - 5}\) produces a negative answer, which many students find counterintuitive.