k + 12 = 336What is the solution to the given equation?

1. INFER the solving strategy

• Given equation: \(\mathrm{k + 12 = 336}\)
• Goal: Find the value of \(\mathrm{k}\) (isolate the variable)
• Strategy: Since 12 is added to \(\mathrm{k}\), use subtraction (the inverse operation) to "undo" the addition

2. INFER the equality principle and apply the inverse operation

• To maintain equality, subtract 12 from both sides:
  \(\mathrm{k + 12 - 12 = 336 - 12}\)
• Left side simplifies: \(\mathrm{k + 12 - 12 = k}\)
• Right side: \(\mathrm{336 - 12 = 324}\)
• Therefore: \(\mathrm{k = 324}\)

Answer: B. 324

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill regarding inverse operations: Students may add 12 to both sides instead of subtracting, thinking they need to "move the 12" by adding it to the other side.

Following this incorrect reasoning: \(\mathrm{k + 12 + 12 = 336 + 12}\), which gives \(\mathrm{k = 348}\).
This may lead them to select Choice C (348).

Second Most Common Error:

Arithmetic execution error: Students understand the correct strategy but make a calculation mistake when computing 336 - 12, potentially getting values that don't match any of the given choices or selecting an incorrect option through careless computation.

The Bottom Line:

This problem tests the fundamental concept that solving equations requires using inverse operations to isolate the variable, along with the critical understanding that whatever you do to one side of an equation, you must do to the other side.