Use the distributive property to remove the parentheses. Simplify. your answer as much as possible. \( 12\left(\frac{3}{4}+2 w\right) \)

To simplify the expression \( 12\left(\frac{3}{4} + 2w\right) \) using the distributive property, follow these steps: **Step 1: Apply the Distributive Property** The distributive property states that \( a(b + c) = ab + ac \). Applying this to the given expression: \[ 12\left(\frac{3}{4} + 2w\right) = 12 \times \frac{3}{4} + 12 \times 2w \] **Step 2: Simplify Each Term** 1. **Multiply 12 by \(\frac{3}{4}\):** \[ 12 \times \frac{3}{4} = \frac{12 \times 3}{4} = \frac{36}{4} = 9 \] 2. **Multiply 12 by \(2w\):** \[ 12 \times 2w = 24w \] **Step 3: Combine the Simplified Terms** \[ 9 + 24w \] **Final Simplified Expression:** \[ 24w + 9 \]