29 = 5y + 9 Which equation has the same solution as the given equation?...

1. INFER the problem strategy

• Given: \(29 = 5\mathrm{y} + 9\)
• Goal: Find an equation with the same solution
• Strategy: Apply algebraic operations to both sides to create an equivalent equation

2. INFER what to isolate first

• To find an equivalent form, isolate the variable term \(5\mathrm{y}\)
• The constant 9 is added to \(5\mathrm{y}\), so subtract 9 from both sides

3. SIMPLIFY the equation step by step

• Start: \(29 = 5\mathrm{y} + 9\)
• Subtract 9 from both sides: \(29 - 9 = 5\mathrm{y} + 9 - 9\)
• Left side: \(29 - 9 = 20\)
• Right side: \(5\mathrm{y} + 9 - 9 = 5\mathrm{y}\)
• Result: \(20 = 5\mathrm{y}\) or \(5\mathrm{y} = 20\)

Answer: B (\(5\mathrm{y} = 20\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors when calculating \(29 - 9\)
Instead of getting 20, they might calculate:

• \(29 - 9 = 18\) (subtraction error)
• \(29 - 9 = 38\) (adding instead of subtracting)

This may lead them to select Choice A (\(5\mathrm{y} = 18\)) or Choice C (\(5\mathrm{y} = 38\))

Second Most Common Error:

Poor INFER reasoning: Students don't recognize that they need to isolate the \(5\mathrm{y}\) term
They might think the answer should just rearrange the original equation without performing operations, or they might add 9 instead of subtracting it.

This causes confusion about which algebraic step to take first and may lead to guessing among the answer choices.

The Bottom Line:

This problem tests whether students understand that equivalent equations are created by applying the same operations to both sides, and whether they can execute basic arithmetic accurately under that principle.