26 + 2 x 8 - 4 / 1 = 14
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, when interchanged in the given equation, make the equation correct. The equation is:
$$26 + 2 \times 8 - 4 \div 1 = 14$$
First, let's evaluate the original expression to see its current value:
$$26 + 2 \times 8 - 4 \div 1$$
Following the order of operations (BODMAS/PEMDAS - Brackets, Orders, Division/Multiplication, Addition/Subtraction):
1. Multiplication: $2 \times 8 = 16$
2. Division: $4 \div 1 = 4$
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 $\times$
The equation becomes:
$$26 + 2 - 8 \times 4 \div 1 = 14$$
Evaluate the left side:
1. Multiplication: $8 \times 4 = 32$
2. Division: $32 \div 1 = 32$
Substitute these values:
$$26 + 2 - 32$$
3. Addition: $26 + 2 = 28$
4. Subtraction: $28 - 32 = -4$
Since $-4 \neq 14$, this option is incorrect.
Option 2: Interchange $=$ and $-$
This means the original '-' sign becomes '=' and the original '=' sign becomes '-'. The equation would be:
$$26 + 2 \times 8 = 4 - 1$$
Evaluate the left side:
1. Multiplication: $2 \times 8 = 16$
2. Addition: $26 + 16 = 42$
Evaluate the right side:
1. Subtraction: $4 - 1 = 3$
Since $42 \neq 3$, this option is incorrect.
Option 3: Interchange $=$ and $\times$
This means the original '×' sign becomes '=' and the original '=' sign becomes '×'. The equation would be:
$$26 + 2 = 8 \times 4 \div 1$$
Evaluate the left side:
1. Addition: $26 + 2 = 28$
Evaluate the right side:
1. Multiplication: $8 \times 4 = 32$
2. Division: $32 \div 1 = 32$
Since $28 \neq 32$, this option is incorrect.
Option 4: Interchange $+$ and $-$
The equation becomes:
$$26 - 2 \times 8 + 4 \div 1 = 14$$
Evaluate the left side:
1. Multiplication: $2 \times 8 = 16$
2. Division: $4 \div 1 = 4$
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 $\boxed{\text{4}}$.
