If 1/2x - 1/6x = 1, what is the value of x?

1. INFER the best approach

• We have an equation with fractions: \(\frac{1}{2}\mathrm{x} - \frac{1}{6}\mathrm{x} = 1\)
• Two main strategies: find common denominator first, or multiply everything by LCD
• Either works - I'll use common denominator approach

2. SIMPLIFY by combining like terms

• Find LCD of 2 and 6, which is 6
• Convert 1/2 to sixths: \(\frac{1}{2} = \frac{3}{6}\)
• Rewrite equation: \(\frac{3}{6}\mathrm{x} - \frac{1}{6}\mathrm{x} = 1\)
• Combine fractions: \(\frac{3-1}{6}\mathrm{x} = \frac{2}{6}\mathrm{x} = \frac{1}{3}\mathrm{x} = 1\)

3. SIMPLIFY to solve for x

• We now have: \(\frac{1}{3}\mathrm{x} = 1\)
• Multiply both sides by 3: \(\mathrm{x} = 3\)

Answer: C. 3

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make errors when combining fractions with different denominators. They might subtract denominators instead of finding a common denominator (getting something like \(\frac{1}{2}\mathrm{x} - \frac{1}{6}\mathrm{x} = \frac{1}{-4}\mathrm{x}\)), or make arithmetic mistakes when finding the LCD.

This can lead to various incorrect calculations and may cause them to select Choice A (-4) or get confused and guess.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly combine the fractions to get \(\frac{1}{3}\mathrm{x} = 1\), but then make an error in the final step. They might divide by 3 instead of multiplying (getting \(\mathrm{x} = \frac{1}{3}\)), or make other algebraic mistakes.

This may lead them to select Choice B (1/3).

The Bottom Line:

This problem tests fundamental fraction arithmetic combined with equation solving. Success requires careful attention to fraction operations and systematic algebraic manipulation - both core algebraic skills that many students rush through.