If 6n = 12, what is the value of n + 4?

1. INFER the solution strategy

• Given information: \(\mathrm{6n = 12}\)
• Target: Find \(\mathrm{n + 4}\)
• Key insight: We can't work directly with \(\mathrm{n + 4}\) until we know what n equals, so we need to solve the equation first

2. SIMPLIFY to solve for n

• Divide both sides of \(\mathrm{6n = 12}\) by 6:
  • \(\mathrm{6n ÷ 6 = 12 ÷ 6}\)
  • \(\mathrm{n = 2}\)

3. SIMPLIFY by substituting into the target expression

• Now substitute \(\mathrm{n = 2}\) into \(\mathrm{n + 4}\):
  • \(\mathrm{n + 4 = 2 + 4 = 6}\)

Answer: 6

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students try to work directly with the expression \(\mathrm{n + 4}\) without realizing they need to find n first.

They might attempt something like "\(\mathrm{6n = 12}\), so \(\mathrm{6(n + 4) = 12 + 24}\)" or similar confused manipulations. This leads to confusion and guessing rather than systematic solution.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify they need to solve for n first, but make arithmetic errors.

For example, they might incorrectly calculate \(\mathrm{12 ÷ 6 = 3}\) (giving \(\mathrm{n = 3}\)), then compute \(\mathrm{3 + 4 = 7}\) as their final answer. This would lead them to select an incorrect answer choice.

The Bottom Line:

This problem tests whether students can break down a two-step process: solve for the variable first, then evaluate the expression. The algebraic steps are straightforward, but students must recognize the logical sequence.