If x = 40, what is the value of x + 6?

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{x = 40}\)
  • We need to find the value of \(\mathrm{x + 6}\)

• What this tells us: We need to substitute the value 40 for x in the expression \(\mathrm{x + 6}\)

2. Substitute and calculate

• Replace x with 40 in the expression \(\mathrm{x + 6}\):

\(\mathrm{x + 6 = 40 + 6 = 46}\)

Answer: C. 46

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the operation sign and calculate \(\mathrm{x - 6}\) instead of \(\mathrm{x + 6}\).

They see "\(\mathrm{x = 40}\)" and "6" in the problem, but misinterpret the plus sign as a minus sign. This leads them to calculate \(\mathrm{40 - 6 = 34}\).

This may lead them to select Choice A (34).

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students understand that \(\mathrm{x = 40}\) but don't recognize they need to add 6 to this value.

They see the question asks for "the value of \(\mathrm{x + 6}\)" but focus only on the "x" part, thinking the answer is simply the value of x itself.

This may lead them to select Choice B (40).

The Bottom Line:

This problem tests whether students can carefully read mathematical expressions and perform basic substitution. The key is paying close attention to the operation being performed (addition, not subtraction) and understanding that finding "\(\mathrm{x + 6}\)" means finding the result after adding 6 to the value of x.