To solve the equation \( \frac{2}{3}x + 6 = 21 \), follow these steps: 1. Subtract 6 from both sides: \[ \frac{2}{3}x = 21 - 6 \] \[ \frac{2}{3}x = 15 \] 2. Multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \): \[ x = 15 \times \frac{3}{2} \] 3. Calculate the right side: \[ x = \frac{15 \times 3}{2} = \frac{45}{2} \] 4. Simplify: \[ x = 22.5 \] Thus, the solution is \[ x = 22.5 \]