x/9 = 18 What is the solution to the given equation?...

1. TRANSLATE the problem goal

• The question asks for 'the solution to the given equation'
• This means: find the value of x that makes the equation \(\mathrm{x/9 = 18}\) true

2. INFER the solving strategy

• Currently x is being divided by 9
• To isolate x, I need to 'undo' this division
• Since division and multiplication are inverse operations, I multiply both sides by 9

3. SIMPLIFY by performing the multiplication

• Left side: \(\mathrm{(x/9) × 9 = x}\) (the 9s cancel out)
• Right side: \(\mathrm{18 × 9 = 162}\)
• Result: \(\mathrm{x = 162}\)

4. Verify the solution

• Substitute \(\mathrm{x = 162}\) back into original equation: \(\mathrm{162/9 = 18}\) ✓

Answer: D (162)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what operation undoes division and perform the wrong operation.

Instead of multiplying by 9, they might add 9 to both sides thinking: '\(\mathrm{x/9 = 18}\), so \(\mathrm{x = 18 + 9 = 27}\).' This comes from confusing equation solving with basic arithmetic operations.

This may lead them to select Choice C (27).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret the relationship shown in the equation.

They might think '\(\mathrm{x/9 = 18}\)' means 'x equals 18 divided by 9' and calculate \(\mathrm{x = 18 ÷ 9 = 2}\), completely misunderstanding that \(\mathrm{x/9}\) is the left side of an equation, not an instruction to divide.

This may lead them to select Choice A (2).

The Bottom Line:

This problem requires students to distinguish between performing arithmetic operations and solving equations. The key insight is recognizing that \(\mathrm{x/9 = 18}\) is a statement of equality that needs to be maintained while isolating \(\mathrm{x}\), not a calculation to be performed.