Final answer:
The inequality 12x > 9(2x - 3) - 15 is solved by distributing, simplifying, and then isolating x, leading to the solution x < 7.
Step-by-step explanation:
To solve the inequality for x, first distribute the 9 on the right side of the inequality.
12x > 9(2x - 3) - 15
12x > 18x - 27 - 15
Now, simplify the right side by combining like terms.
12x > 18x - 42
To get all the x terms on one side, subtract 18x from both sides.
-6x > -42
Now divide both sides by -6, remembering to reverse the inequality sign because you are dividing by a negative number.
x < 7
The solution to the inequality is x < 7.