Let's solve the given equation step by step:

The equation is:
$-9 = \frac{3}{10}c - 3$

Step 1: Isolate the term with $c$ on one side

Add 3 to both sides of the equation: $-9 + 3 = \frac{3}{10}c - 3 + 3$ $-6 = \frac{3}{10}c$

Step 2: Solve for $c$

To eliminate the fraction, multiply both sides by the reciprocal of $\frac{3}{10}$, which is $\frac{10}{3}$: $c = -6 \times \frac{10}{3}$

Simplify the multiplication: $c = \frac{-60}{3}$ $c = -20$

Final Answer:

$c = -20$

Let me know if you'd like a more detailed explanation!

Here are 5 related questions for further exploration:

1. How do you solve equations involving mixed numbers?
2. What happens if the fraction is negative in a similar problem?
3. How can you verify your solution to equations like this one?
4. What is the importance of the reciprocal when solving fractional equations?
5. Can you simplify an equation like this directly without clearing the fraction?

Tip: Always double-check your solution by substituting it back into the original equation to ensure it satisfies the equality!