To simplify the expression \( 17d - 33 + 9(2d + 6) - 11 \), follow these steps:
-
Distribute the \( 9 \) in the term \( 9(2d + 6) \): \[ 9 \times 2d + 9 \times 6 = 18d + 54 \]
-
Substitute this back into the expression: \[ 17d - 33 + 18d + 54 - 11 \]
-
Now, combine like terms. First, combine the \( d \) terms: \[ 17d + 18d = 35d \]
-
Next, combine the constant terms: \[ -33 + 54 - 11 \] \[ -33 + 54 = 21 \] \[ 21 - 11 = 10 \]
-
Put it all together: \[ 35d + 10 \]
Thus, the simplified expression is: \[ \boxed{35d + 10} \]