4x = 48 What is the solution to the given equation? 12 44 52 192...

1. TRANSLATE the problem information

• Given: \(4\mathrm{x} = 48\)
• Find: The value of x that makes this equation true

2. INFER the solution strategy

• To find x, I need to isolate it on one side of the equation
• Since x is being multiplied by 4, I use the inverse operation: division
• I'll divide both sides by 4 to maintain equality

3. SIMPLIFY by performing the division

• \(4\mathrm{x} \div 4 = 48 \div 4\)
• \(\mathrm{x} = 12\)

4. Verify the answer

• Substitute back: \(4(12) = 48\) ✓

Answer: A (12)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse which operation to use when solving equations. Instead of recognizing that division undoes multiplication, they might think "I see 4 and 48, so I'll add them" or "I'll subtract 4 from 48" or even "I'll multiply 48 by 4."

This leads them to calculate:

• \(48 + 4 = 52\), selecting Choice C (52)
• \(48 - 4 = 44\), selecting Choice B (44)
• \(48 \times 4 = 192\), selecting Choice D (192)

The Bottom Line:

The key insight is recognizing that solving equations requires inverse operations - if a variable is being multiplied by a number, you divide by that same number to isolate it. Students who memorize "move the number to the other side" without understanding the underlying inverse relationship often struggle with operation selection.