art A: Describe the error that was made when solving for k. Please write in complete sentences and be specific.

Question

otiginal equation : k/4 + 6 = -2
(4) x K/4 + 6 = -2 x (4)
k+6 = -8
-6 -6
Answer: k = - 14

Answer 1

The error made when solving for \( k \) occurred during the multiplication step. When the original equation \( \frac{k}{4} + 6 = -2 \) was multiplied by 4, the first term should have been \( 4 \times \frac{k}{4} = k \). Instead, it seems there was a misinterpretation, and the text suggests that the equation rewrote to \( k + 6 = -8 \), which is correct. However, there was no mention of the solution from this point being incorrect in the steps provided.

The subtraction step was correctly shown as \( k + 6 - 6 = -8 - 6 \), which leads to \( k = -14 \). Therefore, while the multiplication step was handled correctly, the statement of the procedure lacks clarity about correctly establishing the intermediate equations, and the calculations seem confusing. The conclusion of \( k = -14 \) is correct based on the operations shown, although it could have been presented more clearly.

Answer 2

can you list how to fix the issue

Answer 3

Certainly! To fix the issue in solving the equation \( \frac{k}{4} + 6 = -2 \), you can follow these steps to clarify and ensure the solution is correct:

1. Clear the Equation: Start with the original equation: \[ \frac{k}{4} + 6 = -2 \]

2. Multiply by 4: To eliminate the fraction, multiply the entire equation by 4. It's essential to distribute the multiplication to all terms: \[ 4 \left( \frac{k}{4} \right) + 4(6) = 4(-2) \] This should yield: \[ k + 24 = -8 \]

3. Isolate k: Subtract 24 from both sides to isolate \( k \): \[ k + 24 - 24 = -8 - 24 \] This simplifies to: \[ k = -32 \]

4. Check Your Work: Substitute the value of \( k \) back into the original equation to ensure that the solution is correct: \[ \frac{-32}{4} + 6 = -2 \] Simplifying gives: \[ -8 + 6 = -2 \quad \text{(which is true)} \]

5. Document Steps Clearly: Be careful to lay out each step clearly so that each operation is easy to follow. This helps avoid misunderstandings regarding what operations were performed on which terms.

By following these steps, the solution would correctly yield \( k = -32 \), and the process would be clearer and more understandable.