Solve for the missing divisor using decimal arithmetic: (17.28 ÷ x) / (3.6 × 0.2) = 2. Find x.

Introduction / Context:
This problem tests manipulation of decimal products and ratios. By simplifying the denominator and then isolating x, we can solve without resorting to long division beyond a single clean step.

Given Data / Assumptions:

• Equation: (17.28 ÷ x) / (3.6 × 0.2) = 2.
• All numbers are decimals; aim to minimize decimal complexity.

Concept / Approach:
First evaluate the denominator product. Then convert the compound fraction into a simple equation for 17.28 ÷ x. Finally, invert to find x. Keeping exact decimals prevents rounding errors.

Step-by-Step Solution:
Compute denominator: 3.6 × 0.2 = 0.72.Set (17.28 ÷ x) / 0.72 = 2 ⇒ 17.28 ÷ x = 2 × 0.72 = 1.44.Solve for x: x = 17.28 ÷ 1.44 = 12.

Verification / Alternative check:
Plug back: (17.28/12) = 1.44; 1.44 / 0.72 = 2. The equality holds exactly.

Why Other Options Are Wrong:
120 and 0.12 are order-of-magnitude errors; 1.20 and 0.72 come from misplacing the factor 2 or stopping mid-simplification.

Common Pitfalls:
Multiplying 3.6 by 0.2 incorrectly (should be 0.72); dividing by 2 instead of multiplying; rounding 17.28/1.44 inaccurately.

Final Answer:
12