To simplify the expression \( 8(5x + 1) + 3(9 - x) \), we can distribute the coefficients into the parentheses:
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Distribute \( 8 \) in the first term: \[ 8(5x) + 8(1) = 40x + 8 \]
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Distribute \( 3 \) in the second term: \[ 3(9) - 3(x) = 27 - 3x \]
Now, we can combine the results of the two distributions: \[ 40x + 8 + 27 - 3x \]
Next, we combine like terms (the \( x \) terms and the constant terms):
- For the \( x \) terms: \( 40x - 3x = 37x \)
- For the constant terms: \( 8 + 27 = 35 \)
Putting it all together, we have: \[ 37x + 35 \]
Thus, the simplified expression is: \[ \boxed{37x + 35} \]