If 3x - 8 = 7, what is the value of 3x + 8?

1. TRANSLATE the problem information

• Given equation: \(\mathrm{3x - 8 = 7}\)
• Need to find: \(\mathrm{3x + 8}\)

2. INFER the most efficient approach

• Key insight: We don't need to find x first!
• Since we want \(\mathrm{3x + 8}\) and we have \(\mathrm{3x - 8 = 7}\), we can find \(\mathrm{3x}\) directly
• Once we have \(\mathrm{3x}\), we just add 8 to get our answer

3. SIMPLIFY to find 3x

• Start with: \(\mathrm{3x - 8 = 7}\)
• Add 8 to both sides: \(\mathrm{3x - 8 + 8 = 7 + 8}\)
• This gives us: \(\mathrm{3x = 15}\)

4. SIMPLIFY to find 3x + 8

• We know \(\mathrm{3x = 15}\)
• Therefore: \(\mathrm{3x + 8 = 15 + 8 = 23}\)

Answer: D. 23

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students automatically think they need to solve for x first, so they continue from \(\mathrm{3x = 15}\) to get \(\mathrm{x = 5}\). Then they see 5 in the answer choices and select it without realizing they need to find \(\mathrm{3x + 8}\), not just x.

This leads them to select Choice B (5) instead of recognizing they need to substitute back into the expression \(\mathrm{3x + 8}\).

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when adding 8 + 7 or 15 + 8, or they get confused about which operations to perform on which side of the equation.

This leads to calculation mistakes and may cause them to select Choice A (-1) or Choice C (15) based on their incorrect arithmetic.

The Bottom Line:

This problem tests whether students can work efficiently with algebraic expressions without always needing to find the individual variable. The key insight is recognizing that \(\mathrm{3x + 8}\) is just 8 more than \(\mathrm{3x}\), so once you find \(\mathrm{3x = 15}\), you're almost done!