To solve the equation \(2(5c + 2) - 2c = 3(2c + 3) + 7\), we follow these steps:

### Step 1: Distribute the constants.
\[
2(5c + 2) = 10c + 4
\]
\[
3(2c + 3) = 6c + 9
\]

Substitute these into the equation:
\[
10c + 4 - 2c = 6c + 9 + 7
\]

### Step 2: Combine like terms.
On the left side:
\[
10c - 2c + 4 = 8c + 4
\]
On the right side:
\[
6c + 9 + 7 = 6c + 16
\]
Now the equation is:
\[
8c + 4 = 6c + 16
\]

### Step 3: Isolate the variable.
Subtract \(6c\) from both sides:
\[
8c - 6c + 4 = 16
\]
\[
2c + 4 = 16
\]
Subtract 4 from both sides:
\[
2c = 12
\]

### Step 4: Solve for \(c\).
\[
c = \frac{12}{2} = 6
\]

### Final Answer:
The solution is \(c = 6\).

Would you like more details on any of these steps or have any questions?

Here are 5 related questions:
1. What is the general process for solving linear equations with variables on both sides?
2. How do you handle equations that involve distribution and combining like terms?
3. Can you solve a similar equation with different constants?
4. How can you verify the solution to a linear equation?
5. What are some common mistakes to avoid when solving equations like this?

**Tip:** Always double-check your distribution and combining of like terms to avoid simple errors!

Learn how to solve the equation 2(5c + 2) - 2c = 3(2c + 3) + 7 with a detailed step-by-step solution. This problem involves algebraic concepts such as equations, distribution, and combining like terms. Suitable for students in Grades 7-9.

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