Solve for the missing value in a rational equation: Find ? such that (20 + 8 × 0.5) / (20 − ?) = 12.

Introduction / Context:This item assesses linear equation solving with decimals inside a fraction. The key is to simplify the numerator first, then isolate the denominator expression and solve for the unknown while preserving equality.

Given Data / Assumptions:

• (20 + 8 × 0.5) / (20 − x) = 12
• All arithmetic is exact; no rounding required.

Concept / Approach:Compute the numerator cleanly. Then, cross-multiply (since the denominator is nonzero) to solve for x. Check that the solution does not make the denominator zero and that it satisfies the original equation.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 8 or 2: Do not satisfy 24 / (20 − x) = 12.
• None these: Not applicable because x = 18 works exactly.

Common Pitfalls:

• Forgetting to simplify the numerator before solving.
• Arithmetic slips when subtracting from 20.

Final Answer: