Let's solve the equation step by step:

\[
-3x + 7 - 6(x + 1) = -6x - (2x - 4) + 6
\]

### Step 1: Expand and Simplify Both Sides

Start by distributing the \(-6\) on the left-hand side and the negative sign on the right-hand side:

\[
-3x + 7 - 6x - 6 = -6x - 2x + 4 + 6
\]

Now, simplify by combining like terms on both sides:

\[
-3x - 6x + 7 - 6 = -6x - 2x + 4 + 6
\]

This simplifies to:

\[
-9x + 1 = -8x + 10
\]

### Step 2: Solve for \(x\)

Next, get all the terms involving \(x\) on one side of the equation and the constant terms on the other side. Add \(8x\) to both sides:

\[
-9x + 8x + 1 = 10
\]

\[
-x + 1 = 10
\]

Now, subtract 1 from both sides:

\[
-x = 9
\]

Finally, multiply both sides by \(-1\) to solve for \(x\):

\[
x = -9
\]

### Solution

The solution to the equation is:

\[
x = -9
\]

Would you like further details or explanations?

### Relative Questions:
1. How would the equation change if the term \(-6(x + 1)\) was instead \(-6x + 1\)?
2. What happens if we have an additional constant term on one side of the equation?
3. How do you solve a similar equation like \(-2x + 5 - 3(x + 4) = -7x + 10\)?
4. What is the solution if we change the equation to \( -3x + 7 - 6(x + 1) = -6x + (2x + 4) + 6 \)?
5. How does the solution set change if the equation includes a fractional coefficient?

### Tip:
When solving equations, it's important to combine like terms and simplify both sides as much as possible before isolating the variable.

Learn how to solve the equation -3x + 7 - 6(x + 1) = -6x - (2x - 4) + 6 step-by-step with detailed explanations. This problem involves algebraic simplification, combining like terms, and solving linear equations. Suitable for high school students.

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