Question

Describe the error that was made when solving for k÷4+6=-2

Answer 1

To solve the equation \( \frac{k}{4} + 6 = -2 \), we need to isolate \( k \). Here's how the process should go:

1. **Subtract 6 from both sides**:
\[
\frac{k}{4} + 6 - 6 = -2 - 6
\]
This simplifies to:
\[
\frac{k}{4} = -8
\]

2. **Multiply both sides by 4** to solve for \( k \):
\[
k = -8 \times 4
\]
This results in:
\[
k = -32
\]

If we made an error in this process, it could have occurred during one of the steps:

- **Error in subtraction**: If instead of subtracting 6 from both sides, one mistakenly added 6, that would yield:
\[
\frac{k}{4} = 4 \quad \text{(incorrect)}
\]

- **Error in multiplication**: If during multiplication one made an arithmetic error, like calculating \( -8 \times 4 \) incorrectly, that could lead to a wrong value for \( k \).

In either case, it’s crucial to carefully perform each operation in the correct order to avoid making a mistake. The correct solution to \( k \) is \( -32 \).