To simplify the expression \(8x + 3(x + 5) - 5(x - 4)\), we can follow these steps:
-
Distribute \(3\) in the term \(3(x + 5)\): \[ 3(x + 5) = 3x + 15 \]
-
Distribute \(-5\) in the term \(-5(x - 4)\): \[ -5(x - 4) = -5x + 20 \]
Now substitute these values back into the expression:
\[ 8x + 3x + 15 - 5x + 20 \]
- Combine like terms:
- Combine the \(x\) terms: \[ 8x + 3x - 5x = (8 + 3 - 5)x = 6x \]
- Combine the constant terms: \[ 15 + 20 = 35 \]
Putting it all together, we have: \[ 6x + 35 \]
Thus, the simplified expression is: \[ \boxed{6x + 35} \]