26 + 2 x 8 - 4 / 1 = 14

To solve this problem, we need to find which two signs, when interchanged in the given equation, make the equation correct. The equation is: 26 + 2 × 8 - 4 ÷ 1 = 14 First, let's evaluate the original expression to see its current value: 26 + 2 × 8 - 4 ÷ 1 Following the order of operations (BODMAS/PEMDAS - Brackets, Orders, Division/Multiplication, Addition/Subtraction): 1. Multiplication: 2 × 8 = 16 2. Division: 4 ÷ 1 = 4 Substitute these values back into the expression: 26 + 16 - 4 3. Addition: 26 + 16 = 42 4. Subtraction: 42 - 4 = 38 The current value of the left side is 38, which is not equal to 14. So, we need to interchange signs. Now, let's test each option: Option 1: Interchange - and × The equation becomes: 26 + 2 - 8 × 4 ÷ 1 = 14 Evaluate the left side: 1. Multiplication: 8 × 4 = 32 2. Division: 32 ÷ 1 = 32 Substitute these values: 26 + 2 - 32 3. Addition: 26 + 2 = 28 4. Subtraction: 28 - 32 = -4 Since -4 ≠ 14, this option is incorrect. Option 2: Interchange = and - This means the original '-' sign becomes '=' and the original '=' sign becomes '-'. The equation would be: 26 + 2 × 8 = 4 - 1 Evaluate the left side: 1. Multiplication: 2 × 8 = 16 2. Addition: 26 + 16 = 42 Evaluate the right side: 1. Subtraction: 4 - 1 = 3 Since 42 ≠ 3, this option is incorrect. Option 3: Interchange = and × This means the original '×' sign becomes '=' and the original '=' sign becomes '×'. The equation would be: 26 + 2 = 8 × 4 ÷ 1 Evaluate the left side: 1. Addition: 26 + 2 = 28 Evaluate the right side: 1. Multiplication: 8 × 4 = 32 2. Division: 32 ÷ 1 = 32 Since 28 ≠ 32, this option is incorrect. Option 4: Interchange + and - The equation becomes: 26 - 2 × 8 + 4 ÷ 1 = 14 Evaluate the left side: 1. Multiplication: 2 × 8 = 16 2. Division: 4 ÷ 1 = 4 Substitute these values: 26 - 16 + 4 3. Subtraction: 26 - 16 = 10 4. Addition: 10 + 4 = 14 Since 14 = 14, this option makes the equation correct. Therefore, interchanging the + and - signs makes the equation correct. The final answer is 4.