Let's solve the equation step by step.

The equation is:

\[
2(3x - 9) = -2(-x + 1) + 9x
\]

### Step 1: Distribute the constants on both sides
Expand both sides of the equation by distributing the constants:

\[
2 \times 3x - 2 \times 9 = -2 \times (-x) + (-2 \times 1) + 9x
\]

\[
6x - 18 = 2x - 2 + 9x
\]

### Step 2: Combine like terms
On the right-hand side, combine the \(2x\) and \(9x\):

\[
6x - 18 = 11x - 2
\]

### Step 3: Isolate the variable
Now, let's move all terms involving \(x\) to one side and constant terms to the other side:

\[
6x - 11x = -2 + 18
\]

\[
-5x = 16
\]

### Step 4: Solve for \(x\)
Divide both sides by \(-5\):

\[
x = \frac{16}{-5}
\]

\[
x = -\frac{16}{5}
\]

So, the solution is:

\[
x = -\frac{16}{5}
\]

Would you like further details or have any questions?

Here are 5 related questions you could explore:
1. How do you solve similar equations with fractions?
2. How do you solve equations with more complex distribution?
3. What happens if both sides of the equation have the same variable terms?
4. How do you check your solution in an equation?
5. Can we solve for other variables if given?

**Tip:** Always combine like terms and simplify as much as possible before isolating the variable.

Learn how to solve the linear equation 2(3x−9) = −2(−x+1)+9x using distributive property and combining like terms. This detailed step-by-step solution covers key algebraic concepts, perfect for students in Grades 8-10.

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