Sure, let's solve the inequality -3c - 10(c-2) < 3c + 16 step by step.
First, let's distribute the -10 to the terms inside the parentheses:
-3c - 10c + 20 < 3c + 16
Next, let's combine like terms on both sides:
-13c + 20 < 3c + 16
To isolate the variable c, let's move the 3c term to the left side by subtracting 3c from both sides:
-13c - 3c + 20 < 16
Simplifying further:
-16c + 20 < 16
Now, let's isolate the constant term by subtracting 20 from both sides:
-16c < -4
Finally, to solve for c, we can divide both sides of the inequality by -16. Remember that when dividing or multiplying by a negative number, the inequality sign flips:
c > -4/-16
Simplifying:
c > 1/4
So, the solution to the inequality is c > 1/4.