If x + 7 = 35, what is the value of x + 8?

1. TRANSLATE the problem information

• Given: \(\mathrm{x + 7 = 35}\)
• Find: The value of \(\mathrm{x + 8}\)

2. INFER the most efficient approach

There are two ways to tackle this:

• Option A: Solve for x first, then calculate x + 8
• Option B: Notice that x + 8 is just 1 more than x + 7, so use the relationship directly

3. SIMPLIFY using either approach

Approach A - Solve for x:

• From \(\mathrm{x + 7 = 35}\), subtract 7 from both sides
• \(\mathrm{x = 35 - 7 = 28}\)
• Therefore: \(\mathrm{x + 8 = 28 + 8 = 36}\)

Approach B - Use relationship:

• Since \(\mathrm{x + 7 = 35}\)
• Then \(\mathrm{x + 8 = (x + 7) + 1 = 35 + 1 = 36}\)

Answer: C (36)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may not recognize the elegant relationship method and get stuck trying to solve for x, then make arithmetic errors in the process.

For example, they might miscalculate \(\mathrm{35 - 7 = 27}\) (instead of 28), leading to \(\mathrm{x + 8 = 27 + 8 = 35}\). This may lead them to select Choice C (36) wait, that's actually correct... let me reconsider.

Actually, a more likely error: they calculate \(\mathrm{x = 35 - 7 = 28}\) correctly, but then mistakenly think the answer is just \(\mathrm{x = 28}\), forgetting they need \(\mathrm{x + 8}\). This may lead them to select Choice B (28).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misread the question and think they need to find x instead of \(\mathrm{x + 8}\), stopping their solution process too early.

Since they correctly find \(\mathrm{x = 28}\), this leads them to select Choice B (28).

The Bottom Line:

This problem tests whether students can distinguish between intermediate steps (finding x) and the final answer (finding \(\mathrm{x + 8}\)). The elegant relationship approach (\(\mathrm{x + 8 = x + 7 + 1}\)) provides a nice shortcut, but either method works as long as students answer the actual question being asked.