The given equation becomes correct after interchanging two signs. One of the…

Concept

In an arithmetic equation, every operator (+, −, ×, ÷) is evaluated using the standard order of operations: do all × and ÷ from left to right first, then all + and − from left to right. 'Interchanging two signs' means picking two operator symbols and swapping every occurrence of one for the other throughout the equation, then testing whether the equation evaluates to the stated right-hand side.

Application

The given equation 9 + 5 ÷ 4 × 3 − 6 must equal 12. Swap the ÷ and − symbols everywhere they appear, which turns the equation into 9 + 5 − 4 × 3 ÷ 6, and evaluate using order of operations:

1. Resolve × and ÷ first, left to right: 4 × 3 ÷ 6 = 12 ÷ 6 = 2.

2. Now the expression is 9 + 5 − 2.

3. Resolve + and − left to right: 9 + 5 = 14, then 14 − 2 = 12.

The left-hand side equals 12, which matches the required right-hand side, so swapping ÷ and − is the interchange that fixes the equation.

Cross-check

Testing the other sign-pairs confirms none of them yields 12: swapping + and − gives 9 − 5 ÷ 4 × 3 + 6 = 11.25; swapping + and ÷ gives 9 ÷ 5 + 4 × 3 − 6 = 7.8; swapping ÷ and × gives 9 + 5 × 4 ÷ 3 − 6 ≈ 9.67. Only the ÷ and − swap lands exactly on 12.