Final answer:
To solve the inequality -3|5x-6|+24≥15, the absolute value expression is isolated and two separate inequalities are created. The solutions are x >= 1.8 and x <= 0.6, representing the range outside of which the original inequality holds true.
Step-by-step explanation:
To solve the inequality -3|5x-6|+24≥15, we first isolate the absolute value expression on one side:
- Add 3|5x-6| to both sides: -3|5x-6| + 24 + 3|5x-6| >= 15 + 3|5x-6|, which simplifies to 24 >= 15 + 3|5x-6|.
- Subtract 15 from both sides: 24 - 15 >= 3|5x-6|, which simplifies to 9 >= 3|5x-6|.
- Divide both sides by 3: 9/3 >= |5x-6|, which simplifies to 3 >= |5x-6|.
Next, split the absolute value inequality into two separate inequalities:
- 5x - 6 >= 3 and 5x - 6 <= -3
- For 5x - 6 >= 3: Add 6 to both sides to get 5x >= 9, then divide by 5 to get x >= 9/5 or x >= 1.8.
- For 5x - 6 <= -3: Add 6 to both sides to get 5x <= 3, then divide by 5 to get x <= 3/5 or x <= 0.6.
The two solutions for the inequality are x >= 1.8 and x <= 0.6.