We are given the equation:

\[
-2c + 4x = -6
\]

To solve for \( x \), follow these steps:

1. **Isolate the term with \( x \):**
   
   \[
   4x = -6 + 2c
   \]

2. **Solve for \( x \) by dividing both sides by 4:**

   \[
   x = \frac{-6 + 2c}{4}
   \]

3. Simplify the expression if possible:

   \[
   x = \frac{-6}{4} + \frac{2c}{4}
   \]
   \[
   x = -\frac{3}{2} + \frac{c}{2}
   \]

Thus, the solution is:

\[
x = \frac{c}{2} - \frac{3}{2}
\]

Would you like more details or further explanation?

Here are 5 related questions you could explore:
1. How would the solution change if the equation was \( -2c + 5x = -6 \)?
2. What if the constant on the right side was a different number, like \( -10 \)?
3. How can you check if the solution is correct for specific values of \( c \)?
4. What if we had \( -2c - 4x = -6 \)? How would the steps change?
5. How would the solution change if the coefficient of \( x \) was negative?

**Tip:** Always simplify the expression as much as possible when solving for a variable.

Discover how to solve the linear equation -2c + 4x = -6 with a detailed step-by-step solution. This problem covers essential algebraic concepts, including isolating variables and simplifying expressions. Suitable for students in Grades 8-10.

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