9-2\left(x+4\right)-10\left(25-x+4\right)=5-3x-4\left(x+1\right)

Let's solve the equation:

\[
9 - 2\left(x + 4\right) - 10\left(25 - x + 4\right) = 5 - 3x - 4\left(x + 1\right)
\]

### Step 1: Distribute the terms inside the parentheses
Distribute the \(-2\) and \(-10\) on the left side, and \(-4\) on the right side:

\[
9 - 2x - 8 - 10\left(29 - x\right) = 5 - 3x - 4x - 4
\]

Simplify further:

\[
9 - 2x - 8 - 290 + 10x = 5 - 3x - 4x - 4
\]

Combine like terms:

\[
-2x + 10x - 290 + 1 = -7x + 1
\]

\[
8x - 289 = -7x + 1
\]

### Step 2: Move all terms involving \(x\) to one side
Add \(7x\) to both sides:

\[
15x - 289 = 1
\]

### Step 3: Isolate the variable \(x\)
Add 289 to both sides:

\[
15x = 290
\]

Finally, divide by 15:

\[
x = \frac{290}{15} = \frac{58}{3}
\]

### Solution:
The solution to the equation is \( x = \frac{58}{3} \).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How can you simplify complex linear equations step by step?
2. What techniques can you use when distributing negative coefficients?
3. How do you combine like terms efficiently?
4. What if the coefficients in the equation were fractions?
5. How would you solve this equation if it had multiple variables?
6. What is the next step after isolating the variable when solving linear equations?
7. How do you handle large coefficients when solving equations?
8. What are some common mistakes to avoid when solving linear equations?

**Tip:** When dealing with complex equations, carefully distribute and combine like terms to avoid errors.

Learn how to solve a complex linear equation step-by-step with detailed explanations and examples. This problem involves distributing terms, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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