If 2x = 12, what is the value of 9x?

1. TRANSLATE the problem information

• Given equation: \(\mathrm{2x = 12}\)
• Need to find: \(\mathrm{9x}\)

2. INFER the solution strategy

• To find \(\mathrm{9x}\), I first need to determine the value of x
• Once I know x, I can multiply it by 9

3. SIMPLIFY to solve for x

• Start with: \(\mathrm{2x = 12}\)
• Divide both sides by 2: \(\mathrm{x = 12 \div 2 = 6}\)

4. SIMPLIFY to find 9x

• Now that \(\mathrm{x = 6}\), substitute: \(\mathrm{9x = 9(6) = 54}\)

Answer: 54

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students might try to work directly with \(\mathrm{9x}\) without recognizing they need to find x first. They might attempt to manipulate the original equation \(\mathrm{2x = 12}\) to somehow get \(\mathrm{9x}\) directly, leading to confusion about how the coefficients relate to each other. This leads to abandoning systematic solution and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify that they need to solve for x first, but make arithmetic errors. For example, incorrectly calculating \(\mathrm{12 \div 2 = 5}\), which would lead to \(\mathrm{9x = 9(5) = 45}\), or making errors in the final multiplication step.

The Bottom Line:

This problem tests whether students understand the fundamental principle of substitution - that finding the value of a variable expression requires first solving for the variable itself. The arithmetic is straightforward, but the logical sequence matters.