Question:3x/4 = 6Which equation has the same solution as the given equation?Choose 1 answer:3x = 1.53x = 183x = 243x...

1. TRANSLATE the problem information

• Given equation: \(\frac{3\mathrm{x}}{4} = 6\)
• Need to find: Which equation has the same solution

2. INFER the approach

• Since all answer choices are in the form '\(3\mathrm{x} = [number]\)', I need to isolate \(3\mathrm{x}\) in the original equation
• To eliminate the fraction \(\frac{3\mathrm{x}}{4}\), I should multiply both sides by 4
• This will give me an equation in the same form as the answer choices

3. SIMPLIFY by applying the multiplication property of equality

• Multiply both sides by 4: \(\frac{3\mathrm{x}}{4} \times 4 = 6 \times 4\)
• Left side: \(\frac{3\mathrm{x}}{4} \times 4 = 3\mathrm{x}\)
• Right side: \(6 \times 4 = 24\)
• Result: \(3\mathrm{x} = 24\)

4. INFER the final answer

• The equation \(3\mathrm{x} = 24\) matches choice (C)
• I can verify: if \(3\mathrm{x} = 24\), then \(\mathrm{x} = 8\), and substituting back: \(\frac{3(8)}{4} = \frac{24}{4} = 6\) ✓

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may think they need to 'get rid of' the denominator by dividing instead of multiplying, or they might divide both sides by 4 instead of multiplying.

If they divide both sides by 4: \(\frac{3\mathrm{x}}{4} \div 4 = 6 \div 4\), they get \(\frac{3\mathrm{x}}{16} = 1.5\), then multiply by 16 to get \(3\mathrm{x} = 24\). While this eventually works, the intermediate step creates confusion. Some students might stop at \(\frac{3\mathrm{x}}{16} = 1.5\) and incorrectly think \(3\mathrm{x} = 1.5\).

This may lead them to select Choice A (\(3\mathrm{x} = 1.5\)).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify they should multiply by 4 but make arithmetic errors calculating \(6 \times 4\).

Some might calculate \(6 \times 4\) as 18 (confusing with \(6 \times 3\)) or 6 (forgetting to multiply entirely).

This may lead them to select Choice B (\(3\mathrm{x} = 18\)) or Choice D (\(3\mathrm{x} = 6\)).

The Bottom Line:

This problem tests whether students can systematically apply the multiplication property of equality to transform an equation into an equivalent form, rather than getting distracted by the fraction or making computational mistakes.