Final answer:
To solve the inequality 9x-6(2x-4) <= 5-5(x-7), simplify both sides of the inequality, combine like terms, and isolate the variable x. The solution in interval notation is (-∞, 8].
Step-by-step explanation:
To solve the inequality 9x-6(2x-4)<=5-5(x-7), we can first simplify both sides of the inequality. Distribute the -6 to the terms inside the parentheses: 9x - 12x + 24 <= 5 - 5x + 35. Combine like terms: -3x + 24 <= 40 - 5x. Move all the x terms to one side and all the constant terms to the other side: 2x <= 16. Divide both sides of the inequality by 2: x <= 8. Therefore, the solution in interval notation is (-∞, 8].