To solve the equation \(\frac{2}{3}n - 6 = -8\) using inverse operations, we can follow these steps:
- Add 6 to both sides to eliminate the constant term on the left side:
\[ \frac{2}{3}n - 6 + 6 = -8 + 6 \]
This simplifies to:
\[ \frac{2}{3}n = -2 \]
- Multiply both sides by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\):
\[ n = -2 \cdot \frac{3}{2} \]
Calculating the right side:
\[ n = -3 \]
So, the solution to the equation is:
\[ n = -3 \]
You can verify this by substituting \(n = -3\) back into the original equation:
\[ \frac{2}{3}(-3) - 6 = -2 - 6 = -8 \]
The left side equals the right side, confirming that the solution \(n = -3\) is correct.
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