Final answer:
To solve the inequality, we distributed the 2, combined like terms, and then isolated c to find that c = -10/13.
Step-by-step explanation:
Solving the Inequality for c
To solve the inequality 10c + 2(8c + 10), we need to distribute and combine like terms. Let's work through the steps:
First, we distribute the 2 to the terms inside the parentheses: 10c + 2(8c) + 2(10).
This simplifies to: 10c + 16c + 20.
Next, we combine the like terms: 10c + 16c which equals 26c.
To get c on its own, we subtract 20 from both sides of the inequality, leaving us with 26c = -20.
Finally, we divide both sides by 26 to isolate c. This gives us the solution c = -20/26.
To simplify, we divide the numerator and the denominator by their greatest common divisor, which is 2. The simplest form of the inequality is c = -10/13.
The solution for the inequality in simplest form is c = -10/13.