To solve the equation \(-3x + 6 = 5x - 1\), follow these steps:

1. **Add \(3x\) to both sides** to gather all \(x\) terms on one side:

   \[
   -3x + 3x + 6 = 5x + 3x - 1
   \]

   This simplifies to:

   \[
   6 = 8x - 1
   \]

2. **Add 1 to both sides** to isolate the term with \(x\):

   \[
   6 + 1 = 8x - 1 + 1
   \]

   This simplifies to:

   \[
   7 = 8x
   \]

3. **Divide both sides by 8** to solve for \(x\):

   \[
   \frac{7}{8} = x
   \]

So, the solution to the equation is \( x = \frac{7}{8} \).

Would you like more details or have any questions about this solution?

Here are some related questions you might find helpful:

1. How do you solve linear equations with negative coefficients?
2. What methods can be used to solve equations with variables on both sides?
3. How can you solve an equation if it includes fractions from the beginning?
4. What steps should be taken to verify the solution of an equation?
5. How do different operations affect the balance of an equation?

**Tip:** Always perform the same operation on both sides of the equation to maintain balance and ensure the solution remains valid.

Learn how to solve the linear equation -3x + 6 = 5x - 1 with a step-by-step solution. This problem involves solving for the variable x using basic algebraic operations. Suitable for students in Grades 7-9.

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