4)) Select the expressions that are equivalent to \( -3(t-4) \). \( -4(-3+t) \) \( (-4+t) \cdot-3 \) \( -3(-4+t) \)

To determine which expressions are equivalent to \( -3(t - 4) \), let's first simplify the original expression: \[ -3(t - 4) = -3t + 12 \] Now, let's evaluate each of the given expressions: 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. **\( (-4 + t) \cdot -3 \)** \[ (-4 + t) \cdot -3 = -3(t - 4) = -3t + 12 \] This directly matches the original expression \( -3t + 12 \). 3. **\( -3(-4 + t) \)** \[ -3(-4 + t) = -3(t - 4) = -3t + 12 \] This also directly matches the original expression \( -3t + 12 \). **Conclusion:** The expressions that are equivalent to \( -3(t - 4) \) are: - \( (-4 + t) \cdot -3 \) - \( -3(-4 + t) \) **Therefore, the correct equivalent expressions are the second and third options.** **Answer:** Both the second and third expressions are equivalent to –3(t – 4).