Question:(3x + 9)/3 = 11Which equation has the same solution as the given equation?3x = 333x = 243x = 423x...

1. TRANSLATE the problem information

• Given: We have the equation \(\frac{3\mathrm{x} + 9}{3} = 11\) and need to find which of the four choices has the same solution
• Goal: Find an equation of the form 3x = [number] that gives the same x-value

2. INFER the approach

• To determine which equation has the same solution, we need to solve the original equation for x first
• Then we can check which answer choice gives us the same x-value
• The most efficient approach is to clear the fraction by multiplying both sides by 3

3. SIMPLIFY the original equation

• Multiply both sides by 3: \(3\mathrm{x} + 9 = 33\)
• Subtract 9 from both sides: \(3\mathrm{x} = 33 - 9\)
• Calculate: \(3\mathrm{x} = 24\)
• Therefore: \(\mathrm{x} = 8\)

4. INFER which answer choice matches

• Now check each option to see which gives x = 8:
  • Choice A: \(3\mathrm{x} = 33 → \mathrm{x} = 11\) (not 8)
  • Choice B: \(3\mathrm{x} = 24 → \mathrm{x} = 8\) ✓
  • Choice C: \(3\mathrm{x} = 42 → \mathrm{x} = 14\) (not 8)
  • Choice D: \(3\mathrm{x} = 18 → \mathrm{x} = 6\) (not 8)

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly multiply both sides by 3 to get \(3\mathrm{x} + 9 = 33\), but then forget to subtract 9 from the right side. They incorrectly think the answer is \(3\mathrm{x} = 33\).

This reasoning error happens because students focus on eliminating the fraction but lose track of the multi-step simplification needed afterward.

This may lead them to select Choice A (3x = 33).

Second Most Common Error:

Poor INFER reasoning: Students attempt to manipulate the original equation differently, perhaps trying to distribute the division or making conceptual errors about how fractions work in equations.

This leads to confusion and arithmetic mistakes that don't correspond to any systematic approach.

This causes them to get stuck and guess among the remaining choices.

The Bottom Line:

This problem tests whether students can maintain accuracy through a multi-step algebraic simplification. The key insight is that clearing fractions first (multiplying by 3) creates a simpler equation that's easier to solve systematically.