4x/5 = 20 In the equation above, what is the value of x?...

1. INFER the solution strategy

• Given: \(\frac{4x}{5} = 20\)
• Goal: Isolate x
• Strategy: First eliminate the fraction by multiplying both sides by 5, then divide by the coefficient of x

2. SIMPLIFY by eliminating the fraction

• Multiply both sides by 5:
  • Left side: \(\frac{4x}{5} \times 5 = 4x\)
  • Right side: \(20 \times 5 = 100\)
• Result: \(4x = 100\)

3. SIMPLIFY by isolating x

• Divide both sides by 4:
  • Left side: \(4x \div 4 = x\)
  • Right side: \(100 \div 4 = 25\)
• Result: \(x = 25\)

Answer: A (25)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize the proper sequence of operations to solve the equation. Instead of systematically eliminating the fraction first, they might try random operations like adding the numbers they see (\(4 + 20 = 24\)) or performing operations in the wrong order.

This may lead them to select Choice B (24) or get confused and guess.

Second Most Common Error:

Poor SIMPLIFY execution: Students might understand they need to clear the fraction but execute the operations incorrectly. For example, they might divide 20 by 5 first (getting 4), then multiply by 4 (getting 16), rather than properly multiplying both sides by 5.

This may lead them to select Choice C (16).

The Bottom Line:

Linear equations with fractions require students to think strategically about the order of operations needed to isolate the variable, not just perform random calculations with the numbers they see.