Solve for *c*.



8 − 4*c* = –10 − 6*c* + 10

To solve for \( c \) in the equation \( 8 - 4c = -10 - 6c + 10 \), follow these steps:

1. **Simplify the right-hand side of the equation:**

   \[
   -10 - 6c + 10 = -6c
   \]

   Now the equation is:

   \[
   8 - 4c = -6c
   \]

2. **Add \( 6c \) to both sides of the equation:**

   \[
   8 - 4c + 6c = -6c + 6c
   \]

   Simplifying this, we get:

   \[
   8 + 2c = 0
   \]

3. **Subtract 8 from both sides of the equation:**

   \[
   8 + 2c - 8 = 0 - 8
   \]

   Simplifying this, we get:

   \[
   2c = -8
   \]

4. **Divide both sides by 2 to solve for \( c \):**

   \[
   \frac{2c}{2} = \frac{-8}{2}
   \]

   Simplifying this, we get:

   \[
   c = -4
   \]

So, the solution is \( c = -4 \).

Would you like more details or have any questions?

Here are 8 related questions to expand on this topic:
1. How would you solve the equation \(5 - 3c = -15 - 7c + 15\)?
2. What is the value of \(c\) if the equation was \(9 - 2c = -3 - 5c + 3\)?
3. How do you check if your solution for \(c\) is correct?
4. Can you graph the equations \(8 - 4c\) and \(-10 - 6c + 10\) to visually find the solution?
5. What are the steps to solve a system of linear equations involving \(c\)?
6. How would you solve for \(c\) in the equation \(7c + 5 = 3c - 9\)?
7. Can you explain the difference between solving linear and quadratic equations?
8. How would you solve an equation involving absolute values, such as \(8 - 4|c| = -10 - 6|c| + 10\)?

**Tip:** Always combine like terms and simplify both sides of the equation before isolating the variable.

Learn how to solve the equation 8 - 4c = -10 - 6c + 10 step-by-step. This problem covers linear equations and the process of simplifying equations to isolate variables. Suitable for students in Grades 7-9.

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