If y = 5x + 10, what is the value of y when x = 8?

1. TRANSLATE the problem information

• Given information:
  • Linear equation: \(\mathrm{y = 5x + 10}\)
  • Value to substitute: \(\mathrm{x = 8}\)
  • Need to find: the value of y
• What this tells us: We need to replace x with 8 in the equation and calculate the result.

2. INFER the approach

• This is a direct substitution problem - no complex strategy needed
• Simply replace every x in the equation with 8 and calculate

3. Substitute and calculate

• Replace x with 8: \(\mathrm{y = 5(8) + 10}\)
• Follow order of operations:
  • First: \(\mathrm{5(8) = 40}\)
  • Then: \(\mathrm{40 + 10 = 50}\)

Answer: 50

Why Students Usually Falter on This Problem

Most Common Error Path:

Order of operations confusion: Students might incorrectly group the operations, calculating \(\mathrm{5 × (8 + 10)}\) instead of \(\mathrm{5(8) + 10}\).

Following this incorrect reasoning: \(\mathrm{5 × (8 + 10) = 5 × 18 = 90}\)

This leads to an incorrect answer of 90 instead of the correct answer of 50.

Second Most Common Error:

Weak TRANSLATE reasoning: Students might misunderstand what "when x = 8" means, perhaps thinking they need to solve for x instead of substituting the given value.

This conceptual confusion can lead them to attempt unnecessary algebraic manipulation or become stuck on how to proceed, ultimately resulting in guessing.

The Bottom Line:

This problem tests basic function evaluation skills. Success requires careful attention to order of operations and clear understanding that "when x = 8" is an instruction to substitute, not solve.