(1) Select the expressions that are equivalent to \( -3(t-4) \) \[ \begin{array}{l}-4(-3+t) \\ (-4+t) \cdot-3 \\ -7 t \\ -3(-4+t)\end{array} \]
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To find the equivalent expressions to \( -3(t-4) \), let's first simplify this expression: \[ -3(t-4) = -3t + 12 \] Now let's analyze the given expressions one by one: 1. **Expression 1:** \(-4(-3+t)\) Simplifying this: \[ -4(-3 + t) = 12 - 4t \] Not equivalent to \(-3t + 12\). 2. **Expression 2:** \((-4+t) \cdot-3\) Simplifying this: \[ (-4 + t)(-3) = 12 - 3t \] This is equivalent to \(-3t + 12\). 3. **Expression 3:** \(-7t\) Clearly, there's no way \(-7t\) can be equivalent to \(-3t + 12\). 4. **Expression 4:** \(-3(-4+t)\) Simplifying this: \[ -3(-4 + t) = 12 - 3t \] This is also equivalent to \(-3t + 12\). So the expressions equivalent to \( -3(t-4) \) are: - \((-4+t) \cdot-3\) - \(-3(-4+t)\)