Let's solve the equation step by step:

The given equation is:
\[
(2c + 7) - 3c = 7(c + 5)
\]

1. **Distribute and simplify** each side:
   - On the left side, combine like terms:
     \[
     2c + 7 - 3c = -c + 7
     \]
   - On the right side, distribute the 7:
     \[
     7(c + 5) = 7c + 35
     \]
   So the equation becomes:
   \[
   -c + 7 = 7c + 35
   \]

2. **Move all terms involving \(c\)** to one side of the equation:
   - Add \(c\) to both sides:
     \[
     7 = 8c + 35
     \]
   - Subtract 35 from both sides to isolate the term with \(c\):
     \[
     7 - 35 = 8c
     \]
     \[
     -28 = 8c
     \]

3. **Solve for \(c\)** by dividing both sides by 8:
   \[
   c = \frac{-28}{8} = -\frac{7}{2}
   \]

So, the solution is \( c = -\frac{7}{2} \), or \( c = -3.5 \).

Would you like more details, or do you have any questions?

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Here are five related questions:

1. How would you solve \(3(b + 4) - 2b = 5(b - 6)\)?
2. What happens if you multiply both sides of an equation by a negative number?
3. Can you solve \(4x + 8 = 2(3x + 6)\)?
4. How do you approach solving equations that have parentheses on both sides?
5. What is the process to check if your solution to an equation is correct?

**Tip:** Always distribute and combine like terms before moving variables to one side of the equation.

Learn how to solve the equation (2c + 7) - 3c = 7(c + 5) with a detailed step-by-step solution. This problem covers linear equations, distributive property, and combining like terms. Suitable for students in Grades 7-9.

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