Final answer:
To solve the inequality −6r − 5(−10r + 6) ≤ 3r + 9 + 2r for r, we performed distribution, combined like terms, and isolated r to find that r ≤ 1.
Step-by-step explanation:
The student has asked to solve the inequality for r.
The inequality given is −6r − 5(−10r + 6) ≤ 3r + 9 + 2r. Let's solve it step by step.
- First, distribute the −5 across the terms inside the parenthesis: −6r + 50r − 30 ≤ 3r + 9 + 2r.
- Combine like terms: 44r − 30 ≤ 5r + 9.
- Subtract 5r from both sides to get the r terms on one side: 39r − 30 ≤ 9.
- Add 30 to both sides to get the constant terms on the other: 39r ≤ 39.
- Divide both sides by 39 to solve for r: r ≤ 1.
Thus, the simplest form of the solution to the inequality is r ≤ 1.