Make the equation true by swapping signs — Which interchange of signs makes the equality hold? 5 + 6 ÷ 3 − 12 × 2 = 17

Introduction / Context:We are to interchange two operator symbols everywhere they appear so that the evaluated expression equals 17. Because × and ÷ have higher precedence, interchanging them can drastically change the computed value and is a natural candidate to test.

Given Data / Assumptions:

• Original expression: 5 + 6 ÷ 3 − 12 × 2.
• Goal: value 17.
• We evaluate with standard precedence after performing the chosen global sign swap.

Concept / Approach:Swap '÷' and '×' globally. This changes the division into multiplication and the multiplication into division, potentially balancing the large product term against the rest to reach 17.

Step-by-Step Solution:After swapping '÷' ↔ '×': 5 + 6 × 3 − 12 ÷ 2.Compute: 6 × 3 = 18; 12 ÷ 2 = 6.Now evaluate: 5 + 18 − 6 = 17.Hence the equation is satisfied.

Verification / Alternative check:Swapping '+' and '×' gives 5 × 6 ÷ 3 − 12 + 2 = 10 − 12 + 2 = 0, not 17; so those distractors fail.

Why Other Options Are Wrong:

• '+ and x': produces 0.
• '+ and ÷': yields 5 ÷ 6 × 3 − 12 + 2 ≠ 17.
• '+ and -': merely swaps the final additions/subtractions and cannot fix the large product term.
• 'None of these': unnecessary.

Common Pitfalls:Forgetting to apply the swap to all occurrences or disregarding precedence when re-evaluating the new expression.

Final Answer:÷ and x