Equation Solving: Find the Missing Value

This question asks us to find the value represented by the question mark (?) in the given mathematical equation. The equation involves addition, multiplication, and subtraction.

The equation provided is:

69 + 123 × 2 - 4 = ? + 11

To solve this, we need to follow the standard order of operations, often remembered by the acronyms BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Applying Order of Operations (BODMAS/PEMDAS)

According to the order of operations, multiplication must be performed before addition and subtraction.

• First, calculate the multiplication part: $123 \times 2$.
  • $123 \times 2 = 246$
• Now, substitute this result back into the equation:
  • $69 + 246 - 4 = ? + 11$
• Next, perform the addition and subtraction from left to right on the left side of the equation.
  • Calculate $69 + 246$:
    $69 + 246 = 315$
  • Now the equation is: $315 - 4 = ? + 11$
  • Calculate $315 - 4$:
    $315 - 4 = 311$

Calculating the Missing Value

After simplifying the left side, the equation becomes:

311 = ? + 11

To find the value of '?', we need to isolate it. We can do this by subtracting 11 from both sides of the equation.

• Subtract 11 from both sides:
  • $311 - 11 = (? + 11) - 11$
  • $311 - 11 = ?$
• Perform the subtraction:
  • $300 = ?$

Therefore, the value that comes in place of the question mark (?) is 300.

Verification

We can check our answer by plugging 300 back into the original equation:

Left Side: $69 + 123 \times 2 - 4 = 69 + 246 - 4 = 315 - 4 = 311$.

Right Side: $? + 11 = 300 + 11 = 311$.

Since the left side equals the right side ($311 = 311$), our calculated value for ? is correct.