The equation 20 ÷ 14 + 5 x 20 - 2 = 56 is incorrect due to misused operation signs. By interchanging exactly two signs among ÷, +, x and -, which pair should be swapped so that the equation becomes valid?

Introduction / Context:
This question involves correcting a numerical equation by swapping two operation signs. The numbers are fixed, and we can only change which operations are applied between them by interchanging symbols as suggested in the options. Our goal is to find the swap that makes the equation true.

Given Data / Assumptions:

• Original equation: 20 ÷ 14 + 5 x 20 - 2 = 56.
• We may interchange exactly two of the signs in the entire equation.
• Standard arithmetic precedence (× and ÷ before + and −) applies after swapping.

Concept / Approach:
We test each suggested pair of signs by swapping all of their occurrences throughout the equation, then evaluate the left-hand side. The correct option is the swap that yields exactly 56 on the left while keeping the numbers and their order unchanged.

Step-by-Step Solution:
Option (a): swap + and x. Expression becomes 20 ÷ 14 x 5 + 20 - 2. Evaluate: 20 ÷ 14 x 5 ≈ 7.1429, then plus 20 minus 2 gives a value around 25.14, not 56. Option (b): swap ÷ and -. Every ÷ becomes - and every - becomes ÷. Expression becomes 20 - 14 + 5 x 20 ÷ 2. Evaluate 5 x 20 ÷ 2 first: 5 x 20 = 100, then 100 ÷ 2 = 50. Now compute 20 - 14 = 6, and 6 + 50 = 56. So with this swap the equation becomes 56 = 56, which is true. Option (c): swap + and ÷, or option (d): swap - and +, both lead to left-hand values not equal to 56.

Verification / Alternative check:
Double-checking option (b): after the swap, there is one subtraction, one addition, one multiplication and one division, and the computation steps are clear and unambiguous, leading exactly to 56. No other swap yields that target value.

Why Other Options Are Wrong:
The other swaps produce left-hand expressions that evaluate to values significantly different from 56. Therefore, they cannot make the original equation valid because the numerical equality remains incorrect.

Common Pitfalls:
A frequent error is to swap a sign in only one place instead of all occurrences, or to recompute the expression without respecting the precedence of multiplication and division. Carefully rewriting the entire equation after the swap helps avoid these issues.

Final Answer:
The equation becomes correct when we interchange the signs ÷ and -.