Final answer:
To solve the inequality 9(2x + 1) < 9x - 18, distribute the 9, combine like terms, and solve for x by dividing both sides by 9.
Step-by-step explanation:
To solve the inequality 9(2x + 1) < 9x - 18, we need to simplify and solve for x.
We first distribute the 9 on the left side of the inequality to get 18x + 9 < 9x - 18.
Then, we combine like terms by subtracting 9x from both sides to get 18x - 9x + 9 < -18.
Finally, we subtract 9 from both sides to get 9x < -27. Dividing both sides by 9, we find that x < -3. Therefore, the solution set for x is all values less than -3.