The equation (8x + 4)/3 = 12 has the same solution as which of the following equations?

1. INFER what the problem is asking

• We need to find which equation has the same solution (same x-value) as the given equation
• Strategy: Solve the given equation first, then check which answer choice gives the same x-value

2. SIMPLIFY the given equation \(\frac{8\mathrm{x} + 4}{3} = 12\)

• Multiply both sides by 3: \(8\mathrm{x} + 4 = 36\)
• Subtract 4 from both sides: \(8\mathrm{x} = 32\)
• Divide both sides by 8: \(\mathrm{x} = 4\)

3. SIMPLIFY each answer choice to find which gives x = 4

Choice A: \(2\mathrm{x} + 4 = 9\)

• \(2\mathrm{x} = 5\)
• \(\mathrm{x} = 2.5\) (not our answer)

Choice B: \(2\mathrm{x} + 1 = 9\)

• \(2\mathrm{x} = 8\)
• \(\mathrm{x} = 4\) ✓ (this matches!)

Choice C: \(2\mathrm{x} + 1 = 12\)

• \(2\mathrm{x} = 11\)
• \(\mathrm{x} = 5.5\) (not our answer)

Choice D: \(8\mathrm{x} + 1 = 9\)

• \(8\mathrm{x} = 8\)
• \(\mathrm{x} = 1\) (not our answer)

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors while solving equations, especially when multiplying by 3 or performing basic subtraction/division operations.

For example, they might incorrectly calculate \(8\mathrm{x} + 4 = 36 \Rightarrow 8\mathrm{x} = 40\) instead of \(8\mathrm{x} = 32\), leading to \(\mathrm{x} = 5\). Then when checking answer choices, they might select Choice C (\(\mathrm{x} = 5.5\)) as the closest match, or become confused and guess.

Second Most Common Error:

Poor INFER reasoning: Students misunderstand what "same solution" means and think they need to algebraically transform the original equation to match one of the answer choices exactly.

This leads them to attempt complex manipulations instead of simply solving for x-values. This causes them to get stuck and randomly select an answer without systematic checking.

The Bottom Line:

This problem tests whether students can execute clean algebraic manipulation and understand that equivalent equations are defined by having identical solutions, not identical appearance.