Let's solve the equation step by step:

\[
2c - 12c + 13c = 12
\]

### Step 1: Combine like terms on the left side
Combine the terms involving \(c\):
\[
(2c - 12c + 13c) = (2 - 12 + 13)c = 3c
\]

So the equation becomes:
\[
3c = 12
\]

### Step 2: Solve for \(c\)
Now, divide both sides by 3 to isolate \(c\):
\[
c = \frac{12}{3} = 4
\]

### Final Answer:
\[
c = 4
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What would the solution be for \( 3c - 5c + 10c = 15 \)?
2. How do you solve equations with more variables like \( 2x + 3y = 12 \)?
3. What happens if there are fractions in the equation like \( \frac{1}{2}c - \frac{1}{3}c = 5 \)?
4. How do you factor expressions like \( 2c^2 + 5c - 3 \)?
5. Can you explain the properties of equality used in solving equations?

**Tip:** Always simplify and combine like terms before solving for the unknown variable to make calculations easier.

Discover how to solve the linear equation 2c - 12c + 13c = 12 by combining like terms and applying properties of equality. This step-by-step solution is ideal for students in Grades 6-8, covering key algebraic concepts.

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