Error Analysis: Be sure to answer both Part A and Part B

Question

Part A: Describe the error that was made when solving for k. Please write in complete sentences and be specific.
original equation : k/4 + 6 =-2
(4) x k/4 + 6= -2 x (4)

Answer 1

Part A: The error made when solving for \( k \) in the original equation \( \frac{k}{4} + 6 = -2 \) occurs in the application of the distributive property. The step shown is missing proper parentheses and does not correctly address the components of the equation. Specifically, when multiplying both sides by 4, it should be clearly stated that the entire left side is being multiplied by 4, not just \( \frac{k}{4} \). Instead of writing \( (4) x \frac{k}{4} + 6 = -2 x (4) \), it should explicitly be \( 4 \left(\frac{k}{4} + 6\right) = -2 \cdot 4 \). This is a critical mistake because it leads to an incorrect interpretation of how to apply the multiplication across the terms in the equation.