Select the correct answer. Which algebraic expression is equivalent to the expression below? \[ \begin{array}{ll}3(5 x+7)-6(4-2 x) \\ \begin{array}{ll}\text { O } & 12 x+27 \\ \text { O } & 12 x+3\end{array} \\ \begin{array}{ll}-12\end{array} \\ 27 x-12\end{array} \]

Simplify the expression by following steps: - step0: Subtract the terms: \(3\left(5x+7\right)-6\left(4-2x\right)\) - step1: Expand the expression: \(15x+21-6\left(4-2x\right)\) - step2: Expand the expression: \(15x+21-24+12x\) - step3: Add the terms: \(27x-3\) To simplify the expression \( 3(5x + 7) - 6(4 - 2x) \), we can follow these steps: 1. **Distribute the terms**: - For \( 3(5x + 7) \): \[ 3 \cdot 5x + 3 \cdot 7 = 15x + 21 \] - For \( -6(4 - 2x) \): \[ -6 \cdot 4 + (-6) \cdot (-2x) = -24 + 12x \] 2. **Combine the results**: \[ 15x + 21 - 24 + 12x \] 3. **Combine like terms**: - Combine \( 15x \) and \( 12x \): \[ 15x + 12x = 27x \] - Combine \( 21 \) and \( -24 \): \[ 21 - 24 = -3 \] Thus, the simplified expression is: \[ 27x - 3 \] Now, comparing this with the provided options: - \( 12x + 27 \) - \( 12x + 3 \) - \( -12 \) - \( 27x - 12 \) None of the options match \( 27x - 3 \). Therefore, it seems there might be an error in the options provided. The correct equivalent expression is \( 27x - 3 \).