2.6 + x = 2.8 What value of x is the solution to the given equation?...

1. INFER the solving strategy

• Given: \(\mathrm{2.6 + x = 2.8}\)
• Goal: Find the value of \(\mathrm{x}\)
• Strategy: Since \(\mathrm{2.6}\) is added to \(\mathrm{x}\), we need to subtract \(\mathrm{2.6}\) from both sides to isolate \(\mathrm{x}\)

2. SIMPLIFY by applying inverse operations

• Subtract \(\mathrm{2.6}\) from both sides:
  • Left side: \(\mathrm{2.6 + x - 2.6 = x}\)
  • Right side: \(\mathrm{2.8 - 2.6 = 0.2}\)
• Therefore: \(\mathrm{x = 0.2}\)

3. Consider equivalent forms

• \(\mathrm{0.2}\) can also be written as the fraction \(\mathrm{1/5}\)
• Both forms are acceptable answers

Answer: \(\mathrm{0.2}\) or \(\mathrm{1/5}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may not recognize that they need to perform the inverse operation. Instead of subtracting \(\mathrm{2.6}\), they might add \(\mathrm{2.6}\) to both sides, thinking they need to "move" the \(\mathrm{2.6}\) to the right side.

This leads to: \(\mathrm{2.6 + x + 2.6 = 2.8 + 2.6}\), giving \(\mathrm{x = 5.4}\)

This causes confusion since \(\mathrm{5.4}\) doesn't make sense when substituted back into the original equation.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify that they need to subtract \(\mathrm{2.6}\) from both sides but make an arithmetic error in the subtraction.

Common mistake: \(\mathrm{2.8 - 2.6 = 0.4}\) (instead of \(\mathrm{0.2}\))

This leads to the incorrect answer \(\mathrm{x = 0.4}\), which seems reasonable but is mathematically wrong.

The Bottom Line:

This problem tests fundamental equation-solving skills. Success requires both strategic thinking (knowing to use inverse operations) and careful arithmetic execution.