Solve for \( v \) \[ 0.5(9 v-4)+2=6(0.25 v+2) \] \( v \approx \square \)

To solve for \( v \) in the equation: \[ 0.5(9v - 4) + 2 = 6(0.25v + 2) \] follow these steps: 1. **Expand both sides of the equation:** - **Left Side:** \[ 0.5(9v - 4) + 2 = 0.5 \times 9v - 0.5 \times 4 + 2 = 4.5v - 2 + 2 = 4.5v \] - **Right Side:** \[ 6(0.25v + 2) = 6 \times 0.25v + 6 \times 2 = 1.5v + 12 \] 2. **Set the expanded expressions equal to each other:** \[ 4.5v = 1.5v + 12 \] 3. **Isolate \( v \) by subtracting \( 1.5v \) from both sides:** \[ 4.5v - 1.5v = 12 \implies 3v = 12 \] 4. **Solve for \( v \):** \[ v = \frac{12}{3} = 4 \] **Therefore, the solution is:** \[ v \approx 4 \]