Let's solve the problems step by step:

1. Solve for $x$ in the equation:

$x + 8.63 = 11.001$

To find $x$, subtract 8.63 from both sides: $x = 11.001 - 8.63$ $x = 2.371$

2. Solve for $r$ in the equation:

$0.3r = 2.1$

To solve for $r$, divide both sides of the equation by 0.3: $r = \frac{2.1}{0.3} = 7$

3. Solve for $c$ in the equation:

$|12 - 9 + c| = 12$

First, simplify inside the absolute value: $|3 + c| = 12$

Now, solve for $c$ by considering both possible cases for the absolute value.

Case 1: $3 + c = 12$ $c = 12 - 3$ $c = 9$

Case 2: $3 + c = -12$ $c = -12 - 3$ $c = -15$

So, $c = 9$ or $c = -15$.

Final Answers:

1. $x = 2.371$
2. $r = 7$
3. $c = 9$ or $c = -15$

Would you like further details or clarification on any of these solutions?

Here are some related questions you may find useful:

1. How do you solve equations with fractions or decimals?
2. What is the method for solving absolute value equations?
3. How do you check the solution of an equation?
4. What are the steps in solving linear equations?
5. Can absolute value equations have more than one solution?

Tip: Always check your solution by substituting it back into the original equation to verify if it satisfies the equation.