w + 7 = 357 What value of w is the solution to the given equation?...

1. INFER the solving strategy

• Given: \(\mathrm{w + 7 = 357}\)
• Goal: Find the value of w
• Key insight: Since 7 is added to w, I need to "undo" this addition by subtracting 7 from both sides

2. SIMPLIFY by performing the inverse operation

• Subtract 7 from both sides:
  \(\mathrm{w + 7 - 7 = 357 - 7}\)
• Left side: \(\mathrm{w + 7 - 7 = w}\)
• Right side: \(\mathrm{357 - 7 = 350}\)
• Therefore: \(\mathrm{w = 350}\)

Answer: B. 350

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse this with multiplication equations and think they need to divide by 7 instead of subtract 7.

They might think: "I see w and 7, so I should divide 357 by 7 to get w."
This leads them to calculate \(\mathrm{357 ÷ 7 = 51}\).

This may lead them to select Choice A (51).

Second Most Common Error:

Poor INFER reasoning: Students add 7 instead of subtracting it, thinking they need to "move the 7 to the other side" but forgetting to change the operation.

They calculate: \(\mathrm{w = 357 + 7 = 364}\)

This may lead them to select Choice C (364).

The Bottom Line:

Success on this problem depends on recognizing that addition and subtraction are inverse operations - to "undo" adding 7, you must subtract 7 from both sides.