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

Solution Steps

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

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.

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

1. Add 6 to both sides: $$-3x - 6 + 6 = 15 + 6$$ $$-3x = 21$$
2. Divide both sides by -3: $$x = \frac{21}{-3}$$ $$x = -7$$

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