If x = 7, what is the value of x + 20?

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{x = 7}\)
  • We need to find the value of \(\mathrm{x + 20}\)

• What this tells us: We need to substitute 7 wherever we see x in the expression

2. Substitute and calculate

• Replace x with 7 in the expression \(\mathrm{x + 20}\):

\(\mathrm{x + 20 = 7 + 20 = 27}\)

Answer: C. 27

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what the problem is asking for.

Instead of understanding they need to substitute \(\mathrm{x = 7}\) into \(\mathrm{x + 20}\), they might think the problem is asking them to solve for x, or they might get confused about what "the value of \(\mathrm{x + 20}\)" means. Some students see the equation \(\mathrm{x = 7}\) and think they're done, selecting Choice B (20) because they focus only on the "20" in the expression without performing the substitution.

The Bottom Line:

This is a fundamental substitution problem that tests whether students understand the basic concept of replacing a variable with its given value. The key is recognizing that when \(\mathrm{x = 7}\), every x in any expression should be replaced with 7.