If k = 7, what is the value of 5k - 8? -5 4 27 43...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{k = 7}\)
  • We need to find the value of \(\mathrm{5k - 8}\)

• What this tells us: Replace every k in the expression with 7

2. TRANSLATE the substitution

• Replace k with 7 in the expression \(\mathrm{5k - 8}\)
• This gives us: \(\mathrm{5(7) - 8}\)

3. SIMPLIFY using order of operations

• First, perform the multiplication: \(\mathrm{5(7) = 35}\)
• Then perform the subtraction: \(\mathrm{35 - 8 = 27}\)

Answer: 27 (Choice C)

Why Students Usually Falter on This Problem

Most Common Error Path:

Order of operations confusion: Students might incorrectly group the operations, calculating \(\mathrm{5(k - 8)}\) instead of \(\mathrm{5k - 8}\).

Following this incorrect reasoning: \(\mathrm{5(k - 8) = 5(7 - 8) = 5(-1) = -5}\)

This leads them to select Choice A (−5)

Second Most Common Error:

Sign error during SIMPLIFY: Students might change the subtraction to addition, calculating \(\mathrm{5k + 8}\) instead of \(\mathrm{5k - 8}\).

This gives: \(\mathrm{5(7) + 8 = 35 + 8 = 43}\)

This leads them to select Choice D (43)

The Bottom Line:

While this appears to be a simple substitution problem, it requires careful attention to order of operations and arithmetic signs - fundamental skills that students often rush through, leading to careless errors.