If x = 8, what is the value of 2x - 6?2101422

1. INFER the solution approach

• Given information: \(\mathrm{x = 8}\), and we need to find \(\mathrm{2x - 6}\)
• Strategy: Substitute the known value of x into the expression

2. SIMPLIFY through substitution and calculation

• Replace x with 8: \(\mathrm{2x - 6}\) becomes \(\mathrm{2(8) - 6}\)
• Apply order of operations (multiply first): \(\mathrm{2(8) = 16}\)
• Complete the subtraction: \(\mathrm{16 - 6 = 10}\)

Answer: B (10)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution - Sign confusion: Students change the subtraction to addition

• They calculate: \(\mathrm{2(8) + 6 = 16 + 6 = 22}\)
• This reasoning error transforms the expression from \(\mathrm{2x - 6}\) to \(\mathrm{2x + 6}\)
• This may lead them to select Choice D (22)

Second Most Common Error:

Incomplete INFER reasoning: Students ignore the coefficient and only work with the constant terms

• They focus only on the "x" and the "6": \(\mathrm{x - 6 = 8 - 6 = 2}\)
• They miss that x is multiplied by 2 in the original expression
• This may lead them to select Choice A (2)

The Bottom Line:

This problem tests whether students can systematically substitute and compute while maintaining attention to all parts of an algebraic expression. The most critical skill is methodical execution of each arithmetic step.