To solve the inequality \(5c - 20 \leq 15c + 10\), we can follow these steps:
- First, we'll get all terms involving \(c\) on one side and constant terms on the other side. Start by subtracting \(15c\) from both sides:
\[ 5c - 15c - 20 \leq 10 \]
This simplifies to:
\[ -10c - 20 \leq 10 \]
- Next, add \(20\) to both sides to isolate the term with \(c\):
\[ -10c \leq 10 + 20 \]
This gives:
\[ -10c \leq 30 \]
- Now, divide both sides by \(-10\). Remember that when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign:
\[ c \geq -3 \]
Therefore, the solution to the inequality is:
\[ c \geq -3 \]
In interval notation, this can be written as:
\[ [-3, \infty) \]