Final answer:
To solve the inequality 2x-5 is less than or equal to -x+12, isolate the variable x by adding x to both sides, then adding 5 to both sides, and finally dividing both sides by 3. The solution to the inequality is x <= 5.67, and the interval notation for this solution is (-∞, 5.67].
Step-by-step explanation:
To solve the inequality 2x-5 <= -x+12, we need to isolate the variable x. First, add x to both sides of the inequality to get 3x-5 <= 12. Then, add 5 to both sides to get 3x <= 17. Finally, divide both sides by 3 to get x <= 5.67.
Therefore, the solution to the inequality is x <= 5.67.
The interval notation for this solution is (-∞, 5.67].