Questions: Error Analysis Problem: Solve: −3x−6=15 Student Work: −3x−6=15 −3x+−6=15 3x+6=15 −6 −6 3x/3=9/3 x=3

Error Analysis Problem: Solve: −3x−6=15 Student Work: −3x−6=15 −3x+−6=15 3x+6=15 −6 −6 3x/3=9/3 x=3
Transcript text: Error Analysis Problem: Solv: $|-3 x-6|=15$ Student Work: $|-3 x-6|=15$ $|-3 x|+|-6|=15$ $3 x+6=15$ $\quad-6 \quad-6$ $\frac{3 x}{3}=\frac{9}{3}$ $x=3$
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Solution

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Solution Steps

Step 1: Identify the Problem

The given problem is to solve the absolute value equation: \(|-3x - 6| = 15\).

Step 2: Explain Mistake Made

The student incorrectly simplified the absolute value expression. They treated \(|-3x - 6|\) as \(|-3x| + |-6|\), which is incorrect. Absolute value does not distribute over addition or subtraction.

Step 3: Correct Work and Solution

To solve \(|-3x - 6| = 15\), we need to consider the two cases for the absolute value expression:

Case 1: \(-3x - 6 = 15\)
  1. Add 6 to both sides: \[ -3x - 6 + 6 = 15 + 6 \] \[ -3x = 21 \]
  2. Divide both sides by -3: \[ x = \frac{21}{-3} \] \[ x = -7 \]
Case 2: \(-3x - 6 = -15\)
  1. Add 6 to both sides: \[ -3x - 6 + 6 = -15 + 6 \] \[ -3x = -9 \]
  2. Divide both sides by -3: \[ x = \frac{-9}{-3} \] \[ x = 3 \]

Final Answer

The solutions to the equation \(|-3x - 6| = 15\) are: \[ x = -7 \quad \text{and} \quad x = 3 \]

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