This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve this problem, we need to find which two signs and which two numbers, when interchanged, will make the given equation correct. The original equation is: 8 - 9 × 4 ÷ 6 + 7 = 5 First, let's evaluate the left side of the original equation using the order of operations (BODMAS/PEMDAS): 1. Multiplication: 9 × 4 = 36 2. Division: 36 ÷ 6 = 6 Substitute these values back into the expression: 8 - 6 + 7 3. Subtraction: 8 - 6 = 2 4. Addition: 2 + 7 = 9 So, the original equation evaluates to 9 = 5, which is incorrect. We need to find an interchange that results in 5. Now, let's test each option: Option 1: Interchange + and -, and 9 and 6 The equation becomes: 8 + 6 × 4 ÷ 9 - 7 = 5 Evaluate the left side: 1. Multiplication: 6 × 4 = 24 2. Division: 24 ÷ 9 = (24)/(9) = (8)/(3) Substitute these values: 8 + (8)/(3) - 7 1 + (8)/(3) = (3)/(3) + (8)/(3) = (11)/(3) Since (11)/(3) ≠ 5, this option is incorrect. Option 2: Interchange + and -, and 8 and 7 The equation becomes: 7 - 9 × 4 ÷ 6 + 8 = 5 Evaluate the left side: 1. Multiplication: 9 × 4 = 36 2. Division: 36 ÷ 6 = 6 Substitute these values: 7 - 6 + 8 3. Subtraction: 7 - 6 = 1 4. Addition: 1 + 8 = 9 Wait, I made a mistake in my scratchpad. Let's re-evaluate this option carefully. Original: 8 - 9 × 4 ÷ 6 + 7 = 5 Interchange + and - : 8 + 9 × 4 ÷ 6 - 7 = 5 Interchange 8 and 7: 7 + 9 × 4 ÷ 6 - 8 = 5 Evaluate the left side of the modified equation: 7 + 9 × 4 ÷ 6 - 8 1. Multiplication: 9 × 4 = 36 2. Division: 36 ÷ 6 = 6 Substitute these values: 7 + 6 - 8 3. Addition: 7 + 6 = 13 4. Subtraction: 13 - 8 = 5 Since 5 = 5, this option makes the equation correct. Option 3: Interchange × and ÷, and 6 and 7 The equation becomes: 8 - 9 ÷ 4 × 7 + 6 = 5 Evaluate the left side: 1. Division: 9 ÷ 4 = (9)/(4) 2. Multiplication: (9)/(4) × 7 = (63)/(4) Substitute these values: 8 - (63)/(4) + 6 14 - (63)/(4) = (56)/(4) - (63)/(4) = -(7)/(4) Since -(7)/(4) ≠ 5, this option is incorrect. Option 4: Interchange ÷ and +, and 8 and 7 The equation becomes: 7 - 9 × 4 + 6 ÷ 8 = 5 Evaluate the left side: 1. Multiplication: 9 × 4 = 36 2. Division: 6 ÷ 8 = (6)/(8) = (3)/(4) Substitute these values: 7 - 36 + (3)/(4) -29 + (3)/(4) = -(116)/(4) + (3)/(4) = -(113)/(4) Since -(113)/(4) ≠ 5, this option is incorrect. Therefore, interchanging the + and - signs, and the numbers 8 and 7 makes the equation correct. The final answer is 2.