If x/3 = 8, what is the value of x - 5?

1. SIMPLIFY the given equation to find x

• Given: \(\frac{\mathrm{x}}{3} = 8\)
• To isolate x, multiply both sides by 3:
  • \(\frac{\mathrm{x}}{3} \times 3 = 8 \times 3\)
  • \(\mathrm{x} = 24\)

2. INFER what the problem is actually asking for

• The question asks for "the value of x - 5"
• Now that we know \(\mathrm{x} = 24\), we need to calculate \(\mathrm{x} - 5\)

3. SIMPLIFY the final expression

• Substitute \(\mathrm{x} = 24\) into \(\mathrm{x} - 5\):
  • \(\mathrm{x} - 5 = 24 - 5 = 19\)

Answer: 19

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students correctly identify that they need to multiply both sides by 3, but make arithmetic errors.

They might calculate \(8 \times 3\) incorrectly (getting 21 instead of 24) or make a subtraction error with \(24 - 5\). If they get \(\mathrm{x} = 21\), they would calculate \(21 - 5 = 16\), leading them to select Choice B (16).

Second Most Common Error:

Poor INFER reasoning: Students solve correctly for \(\mathrm{x} = 24\), but then answer with just the value of x instead of \(\mathrm{x} - 5\).

They stop after finding \(\mathrm{x} = 24\) and don't recognize that the problem asks for \(\mathrm{x} - 5\), not just x. This leads them to select Choice D (24).

The Bottom Line:

This is a straightforward two-step problem, but success requires both careful arithmetic execution and attention to exactly what the question is asking for. Students must resist the temptation to stop once they find x.