To simplify the expression \( 7(4 + t) - 3(t + 3) \), follow these steps:
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Distribute \( 7 \) in the first term: \[ 7(4) + 7(t) = 28 + 7t \]
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Distribute \( -3 \) in the second term: \[ -3(t) - 3(3) = -3t - 9 \]
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Combine the results from steps 1 and 2: \[ 28 + 7t - 3t - 9 \]
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Combine like terms:
- The constant terms: \( 28 - 9 = 19 \)
- The \( t \) terms: \( 7t - 3t = 4t \)
Putting it all together, the expression simplifies to: \[ 19 + 4t \]
So, the final answer is: \[ \boxed{4t + 19} \]