To simplify the expression \(1.5(3x + 4) + 0.25(6x + 8)\), we will distribute the constants into the parentheses first:
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Distributing \(1.5\): \[ 1.5(3x) + 1.5(4) = 4.5x + 6 \]
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Distributing \(0.25\): \[ 0.25(6x) + 0.25(8) = 1.5x + 2 \]
Now, we will combine the two results: \[ (4.5x + 6) + (1.5x + 2) \]
Next, we combine like terms:
- Combine the \(x\) terms: \[ 4.5x + 1.5x = 6x \]
- Combine the constant terms: \[ 6 + 2 = 8 \]
Putting it all together, we have: \[ 6x + 8 \]
So, the simplified expression is: \[ \boxed{6} ; x + \boxed{8} \]
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