Let's solve the inequality step by step:
Given:
\[ 15 + 12c \geq 9(c + 15) \]
- First, distribute the \(9\) on the right side:
\[ 15 + 12c \geq 9c + 135 \]
- Next, we want to isolate the terms involving \(c\) on one side. To do that, subtract \(9c\) from both sides:
\[ 15 + 12c - 9c \geq 135 \]
This simplifies to:
\[ 15 + 3c \geq 135 \]
- Now, subtract \(15\) from both sides:
\[ 3c \geq 120 \]
- Next, divide both sides by \(3\):
\[ c \geq 40 \]
Thus, the solution to the inequality is:
c ≥ 40