Let's solve the equation step by step:

### Given equation:

\[
7x - 3(9x + 4) = 9(-x - 1) + x
\]

### Step 1: Expand both sides

Expand both sides by distributing the constants inside the parentheses.

On the left-hand side:
\[
7x - 3(9x + 4) = 7x - (27x + 12) = 7x - 27x - 12
\]
Simplify:
\[
7x - 27x - 12 = -20x - 12
\]

On the right-hand side:
\[
9(-x - 1) + x = -9x - 9 + x
\]
Simplify:
\[
-9x + x - 9 = -8x - 9
\]

### Step 2: Combine like terms

Now we have:
\[
-20x - 12 = -8x - 9
\]

### Step 3: Move terms with \(x\) to one side

Add \(8x\) to both sides:
\[
-20x + 8x - 12 = -9
\]
Simplify:
\[
-12x - 12 = -9
\]

### Step 4: Move constant terms to the other side

Add 12 to both sides:
\[
-12x = 3
\]

### Step 5: Solve for \(x\)

Divide both sides by \(-12\):
\[
x = \frac{3}{-12} = -\frac{1}{4}
\]

### Final Answer:
\[
x = -\frac{1}{4}
\]

Would you like further explanation or help with a similar problem?

**Related Questions:**
1. How do you handle equations with variables on both sides?
2. How can you check your solution for an equation?
3. What are common mistakes to avoid when solving linear equations?
4. What are some real-world applications of solving equations like this?
5. How do you solve equations with fractions or decimals?

**Tip:** Always combine like terms and simplify the equation as much as possible before moving terms to one side!

Learn how to solve the linear equation 7x - 3(9x + 4) = 9(-x - 1) + x step by step. This problem covers essential algebraic concepts like the distributive property and combining like terms. Suitable for students in Grades 8-10.

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