To solve the equation \( \frac{2}{3}x - 5 = 27 \), we can proceed with the following steps:
Step 1: Add 5 to both sides of the equation.
This gives us:
\[
\frac{2}{3}x - 5 + 5 = 27 + 5
\]
\[
\frac{2}{3}x = 32
\]
Step 2: Multiply both sides of the equation by \( \frac{3}{2} \).
This gives us:
\[
\frac{3}{2} \cdot \frac{2}{3}x = 32 \cdot \frac{3}{2}
\]
\[
x = 48
\]
Solution: \( x = 48 \)
Summary of Steps:
- Step 1: Add 5 to both sides.
- Step 2: Multiply both sides by \( \frac{3}{2} \).
The solution is \( x = 48 \).