(1) Select the expressions that are equivalent to \( -3(t-4) \) \[ \begin{array}{l}-4(-3+t) \\ (-4+t) \cdot-3 \\ -7 t \\ -3(-4+t)\end{array} \]

To determine which expressions are equivalent to \( -3(t - 4) \), let's simplify each option: 1. **\(-4(-3 + t)\)** \[ -4(-3 + t) = -4(t - 3) = -4t + 12 \] This simplifies to \(-4t + 12\), which is **not** the same as \(-3t + 12\). 2. **\((-4 + t) \cdot -3\)** \[ (-4 + t) \cdot -3 = (t - 4) \cdot -3 = -3t + 12 \] This simplifies to \(-3t + 12\), which **matches** \(-3(t - 4)\). 3. **\(-7t\)** \[ -7t \] This is simply \(-7t\), which does **not** match \(-3t + 12\). 4. **\(-3(-4 + t)\)** \[ -3(-4 + t) = -3(t - 4) = -3t + 12 \] This simplifies to \(-3t + 12\), which **matches** \(-3(t - 4)\). **Therefore, the expressions that are equivalent to \( -3(t - 4) \) are:** - \((-4 + t) \cdot -3\) - \(-3(-4 + t)\) **Final Answer:** Both \((-4 + t) \cdot -3\) and \(-3(-4 + t)\) are equivalent to \(-3(t-4)\).