Answer:
To solve the inequality 12 − 6r ≤ 3(5 + r) for r, we can follow these steps:
1. Distribute the 3 to the terms inside the parentheses:
12 − 6r ≤ 15 + 3r
2. Simplify the inequality by combining like terms:
12 ≤ 15 + 3r + 6r
3. Combine the r terms on the right side of the inequality:
12 ≤ 15 + 9r
4. Subtract 15 from both sides to isolate the term with r:
12 - 15 ≤ 15 - 15 + 9r
-3 ≤ 9r
5. Divide both sides of the inequality by 9 to solve for r:
-3/9 ≤ 9r/9
-1/3 ≤ r
So, the solution to the inequality is r ≤ -1/3. This means that any value of r that is less than or equal to -1/3 will satisfy the given inequality.
Explanation: