-3x+7-6(x+1)=-6x-(2x-4)+6 whats the solution set

Let's solve the equation step by step and find the solution set.

### Original Equation:

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

### Step 1: Distribute and Simplify Both Sides

Expand the expressions:

- On the left-hand side:
  \[
  -3x + 7 - 6(x + 1) = -3x + 7 - 6x - 6
  \]
  Simplify it further:
  \[
  -9x + 1
  \]

- On the right-hand side:
  \[
  -6x - (2x - 4) + 6 = -6x - 2x + 4 + 6
  \]
  Simplify it further:
  \[
  -8x + 10
  \]

So, the equation now becomes:

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

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

Get all terms involving \( x \) on one side of the equation and constant terms on the other side:

Add \( 8x \) to both sides:

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

Simplify:

\[
-x + 1 = 10
\]

Subtract 1 from both sides:

\[
-x = 9
\]

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

\[
x = -9
\]

### Step 3: Solution Set

The solution set is:

\[
\{ -9 \}
\]

This means the only value that satisfies the equation is \( x = -9 \).

Would you like further details or explanations?

### Relative Questions:
1. What if the equation was \( -3x + 7 - 6(x + 1) = -6x + (2x - 4) + 6 \)?
2. How do you solve a similar equation \( -4x + 5 - 3(x - 2) = -7x + 8 \)?
3. What happens if there's an additional term on one side of the equation?
4. How does the solution change if the equation involves a quadratic term?
5. What if the right-hand side had a constant term subtracted instead of added?

### Tip:
Always check your final solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation -3x + 7 - 6(x + 1) = -6x - (2x - 4) + 6 step-by-step with a detailed solution. This problem involves algebraic manipulation, distribution, and solving linear equations. Suitable for high school students studying algebra.

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