Solve Equation with Missing Value

This question requires us to find the number that replaces the question mark ('?') in the given mathematical equation. To solve this correctly, we must follow the standard order of operations, often remembered by the acronym BODMAS/PEMDAS.

Understanding Order of Operations (BODMAS/PEMDAS)

BODMAS stands for:

• Brackets
• Order (powers and roots)
• Division
• Multiplication
• Addition
• Subtraction

PEMDAS is similar: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Multiplication and Division have the same priority, and we solve them from left to right. Similarly, Addition and Subtraction have the same priority, solved from left to right.

Step-by-Step Calculation

The given equation is:

10 + ? × 6 ÷ 2 = 46

Let's replace the question mark '?' with a variable, say x:

10 + x × 6 ÷ 2 = 46

1. Apply BODMAS/PEMDAS: First, we handle multiplication and division from left to right. In our equation, we have multiplication (x × 6) and division (6 ÷ 2). According to the left-to-right rule for operations of the same priority, we perform the division first:

   6 ÷ 2 = 3

   The equation now becomes:

   10 + x × 3 = 46

2. Next Operation: Now, we perform the multiplication:

   x × 3 = 3x

   The equation simplifies to:

   10 + 3x = 46

3. Isolate the Variable Term: To find the value of x, we first need to isolate the term containing x (which is 3x). We do this by subtracting 10 from both sides of the equation:

   3x = 46 - 10

   3x = 36

4. Solve for x: Finally, we solve for x by dividing both sides by 3:

   x = 36 ÷ 3

   x = 12

Conclusion

The value that should replace the question mark '?' in the equation is 12.

We can check this:

10 + 12 × 6 ÷ 2

= 10 + 12 × 3 (Division first: 6 ÷ 2 = 3)

= 10 + 36 (Multiplication next: 12 × 3 = 36)

= 46 (Addition last)

This matches the right side of the original equation. Therefore, the missing value is 12.