If t = 4u, which of the following is equivalent to 2t?

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{t = 4u}\)
  • Need to find what \(\mathrm{2t}\) equals
• This is asking us to find an equivalent expression for \(\mathrm{2t}\)

2. INFER the solution approach

• Since we know \(\mathrm{t = 4u}\), we can substitute this value directly into \(\mathrm{2t}\)
• Strategy: Replace t with 4u in the expression \(\mathrm{2t}\)

3. SIMPLIFY through substitution and multiplication

• \(\mathrm{2t = 2(4u)}\)
• \(\mathrm{2t = 8u}\)

Answer: A. 8u

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic mistakes when handling the multiplication, particularly with the coefficient 2.

Some students might incorrectly think: "If \(\mathrm{t = 4u}\), then \(\mathrm{2t}\) means divide by 2, so \(\mathrm{2t = 4u ÷ 2 = 2u}\)." This fundamental misunderstanding of what "\(\mathrm{2t}\)" means (2 times t, not t divided by 2) leads them to select Choice B (2u).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret what "\(\mathrm{2t}\)" represents or get confused about the direction of the substitution.

This confusion about the notation or the substitution process causes them to get stuck and abandon systematic solution, leading to guessing among the remaining choices.

The Bottom Line:

This problem tests whether students understand that \(\mathrm{2t}\) means "2 times t" and can correctly substitute one expression for another. The key insight is recognizing that substitution is direct replacement followed by straightforward multiplication.