If 7x = 28, what is the value of 8x?

1. TRANSLATE the problem information

• Given: \(\mathrm{7x = 28}\)
• Find: The value of \(\mathrm{8x}\)

2. INFER the solution strategy

• Key insight: We can't directly find \(\mathrm{8x}\) without knowing what x equals
• Strategy: First solve for x, then substitute that value into \(\mathrm{8x}\)

3. SIMPLIFY to find x

• From \(\mathrm{7x = 28}\), divide both sides by 7:
• \(\mathrm{x = 28 ÷ 7 = 4}\)

4. SIMPLIFY to find 8x

• Substitute \(\mathrm{x = 4}\) into the expression \(\mathrm{8x}\):
• \(\mathrm{8x = 8(4) = 32}\)

Answer: B. 32

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students attempt to find a direct relationship between \(\mathrm{7x}\) and \(\mathrm{8x}\) without solving for x first.

Some students might think: "Since 8 is 1 more than 7, then \(\mathrm{8x}\) should be 1 more than \(\mathrm{7x}\), so \(\mathrm{8x = 28 + 1 = 29}\)." Others might try ratio thinking: "\(\mathrm{8/7}\) times as much as \(\mathrm{7x}\) means \(\mathrm{8x = (8/7) × 28 = 32}\)." While this ratio approach actually works, students often make calculation errors or set up the ratio incorrectly.

This leads to confusion and incorrect answer selection.

The Bottom Line:

The cleanest, most reliable approach is the two-step method: solve for the variable first, then substitute. Students who try shortcuts often make conceptual or computational errors.