Error Analysis Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Find the error: a student solves 2(x+3)=102(x+3) = 10 by writing 2x+3=102x+3=10, then x=3.5x=3.5. What went wrong?

Solution

  1. 1
    Error: the student did not distribute the 2 correctly. The correct expansion is 2(x+3)=2x+62(x+3) = 2x+6, not 2x+32x+3.
  2. 2
    Correct solution: 2x+6=10ā‡’2x=4ā‡’x=22x+6=10 \Rightarrow 2x=4 \Rightarrow x=2.
  3. 3
    Check: 2(2+3)=2(5)=102(2+3)=2(5)=10. Confirmed.

Answer

x=2Ā (errorĀ wasĀ failingĀ toĀ distributeĀ 2Ā toĀ bothĀ termsĀ inĀ theĀ bracket)x = 2 \text{ (error was failing to distribute 2 to both terms in the bracket)}
The distributive law requires multiplying every term inside the brackets. Forgetting to multiply the constant term is one of the most frequent algebra errors.

About Error Analysis

The systematic study of how errors arise in calculations or models, how large they are, and how they propagate through subsequent steps.

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More Error Analysis Examples

Example 1 easy

A student writes: '[formula].' Identify the error and find a numerical counterexample.

Example 2 medium

A student 'proves': '[formula] for all [formula]' by checking [formula]. Identify the error in this

Example 4 medium

A student cancels incorrectly: [formula]. Identify and correct the error.

ā† All Error Analysis Examples Error Analysis Concept