16x + 30 = 190 Which equation has the same solution as the given equation?...

1. INFER what the question is asking

• We need to find which equation has the same solution as \(16x + 30 = 190\)
• This means finding an equivalent equation through algebraic manipulation

2. SIMPLIFY the given equation to match the answer format

• Given: \(16x + 30 = 190\)
• All answer choices are in the form "16x = [number]"
• To get this format, subtract 30 from both sides:
  \(16x + 30 - 30 = 190 - 30\)
  \(16x = 160\)

3. INFER the correct answer

• The equation \(16x = 160\) is equivalent to the original equation
• Looking at the choices, this matches Choice C

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make arithmetic errors when subtracting 30 from 190, getting 130 instead of 160.

They correctly understand they need to subtract 30 from both sides, but calculate \(190 - 30 = 130\) (perhaps confusing it with \(160 - 30 = 130\)). This may lead them to select Choice B (\(16x = 130\)).

Second Most Common Error:

Poor INFER reasoning: Students don't understand what "same solution" means and think they need to somehow use the number 190.

They might think the equivalent equation should still contain 190 somewhere, leading them to select Choice D (\(16x = 190\)) without performing any algebraic manipulation.

The Bottom Line:

This problem tests whether students can perform basic algebraic manipulation accurately and understand that equivalent equations are created through valid algebraic operations, not by changing random numbers.