To solve the equation \( \frac{k}{4} + 6 = -2 \), we need to isolate \( k \). Here's how the process should go:
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Subtract 6 from both sides: \[ \frac{k}{4} + 6 - 6 = -2 - 6 \] This simplifies to: \[ \frac{k}{4} = -8 \]
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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:
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Error in subtraction: If instead of subtracting 6 from both sides, one mistakenly added 6, that would yield: \[ \frac{k}{4} = 4 \quad \text{(incorrect)} \]
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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 \( -32 \).