To solve the equation \( \frac{2}{3}n - 6 = -8 \) using inverse operations, follow these steps:
Step 1: Isolate the term with the variable
First, we need to eliminate the constant term on the left side. We can do this by adding 6 to both sides of the equation:
\[ \frac{2}{3}n - 6 + 6 = -8 + 6 \]
Simplifying both sides gives:
\[ \frac{2}{3}n = -2 \]
Step 2: Solve for \( n \)
Next, we need to get \( n \) by itself. To do this, we can multiply both sides of the equation by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[ \frac{3}{2} \cdot \frac{2}{3}n = -2 \cdot \frac{3}{2} \]
The left side simplifies as follows:
\[ 1n = -2 \cdot \frac{3}{2} \]
Now calculating the multiplication on the right:
\[ n = -2 \cdot \frac{3}{2} = -\frac{6}{2} = -3 \]
So the solution to the equation is:
\[ n = -3 \]
Step 3: Check the Answer
To verify our solution, we will substitute \( n = -3 \) back into the original equation:
\[ \frac{2}{3}(-3) - 6 = -8 \]
Calculating the left side, we have:
\[ \frac{2 \cdot -3}{3} - 6 = -2 - 6 = -8 \]
This matches the right side of the equation, confirming our solution is correct.
Final Answer
The solution is \( n = -3 \).