If 3x = 30, what is the value of 3x - 12?

1. TRANSLATE the problem information

• Given: \(\mathrm{3x = 30}\)
• Find: the value of \(\mathrm{3x - 12}\)
• What this tells us: We have the value of \(\mathrm{3x}\) already, so we can use it directly

2. INFER the most efficient approach

• Since we know \(\mathrm{3x = 30}\), we don't need to solve for x first
• We can substitute the known value of \(\mathrm{3x}\) directly into our target expression
• Strategy: Replace \(\mathrm{3x}\) with \(\mathrm{30}\) in the expression \(\mathrm{3x - 12}\)

3. SIMPLIFY by substitution

• \(\mathrm{3x - 12}\) becomes: \(\mathrm{30 - 12 = 18}\)

Answer: B. 18

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skills: Students misread the target expression and solve for the wrong thing.

They might solve for x first (getting \(\mathrm{x = 10}\)), then calculate:

• \(\mathrm{x - 12 = 10 - 12 = -2}\), leading to Choice A (-2)
• \(\mathrm{x + 12 = 10 + 12 = 22}\), leading to Choice C (22)
• \(\mathrm{3x + 12 = 30 + 12 = 42}\), leading to Choice D (42)

The Bottom Line:

This problem tests your ability to work with expressions efficiently. The key insight is that you don't always need to solve for the individual variable when you already have the value of the expression you need (\(\mathrm{3x = 30}\)).