Final answer:
The solution to the inequality 9(2x + 1) < 9x – 18 is all real numbers x such that x < – 3. This is found by distributing the 9, moving all x terms to one side, constants to the other, simplifying, and dividing by 9.
Step-by-step explanation:
The student has asked for the solution set of the inequality 9(2x + 1) < 9x – 18. To find the value of x that satisfies this inequality, follow these steps:
- Distribute the 9 on the left side of the inequality: 18x + 9 < 9x – 18.
- Move all terms involving x to one side and constants to the other side: 18x – 9x < – 18 – 9.
- Simplify both sides of the inequality: 9x < – 27.
- Divide both sides by 9 to solve for x: x < – 3.
Therefore, the solution set for the inequality is all values of x that are less than – 3. This can be represented on a number line where every point to the left of – 3 is shaded to show the values that x can take within the solution set.