Let's solve the equation step by step:

The given equation is:

\[
4x - (x - 4) = 5x + 3(x - 35)
\]

### Step 1: Simplify both sides

First, distribute the negative sign on the left side and the \(3\) on the right side:

\[
4x - x + 4 = 5x + 3x - 105
\]

Simplify further:

\[
(4x - x) + 4 = (5x + 3x) - 105
\]

\[
3x + 4 = 8x - 105
\]

### Step 2: Move terms involving \(x\) to one side

Now, subtract \(3x\) from both sides:

\[
3x + 4 - 3x = 8x - 105 - 3x
\]

\[
4 = 5x - 105
\]

### Step 3: Solve for \(x\)

Next, add \(105\) to both sides:

\[
4 + 105 = 5x - 105 + 105
\]

\[
109 = 5x
\]

Finally, divide by \(5\) to get \(x\):

\[
x = \frac{109}{5}
\]

\[
x = 21.8
\]

### Final Answer:

\[
x = 21.8
\]

Would you like more details or have any questions about the steps?

Here are 5 related questions for further practice:
1. Solve \(3x - (2x - 7) = 4x + 6\).
2. Find \(x\) if \(6x - (x + 5) = 2x + 3(2x - 4)\).
3. Solve \(2(x - 4) + 5 = 4x + 3(x - 7)\).
4. What is the solution to \(7x - 2(x + 3) = 5x + 18\)?
5. Solve \(4(x + 3) - 2(x - 5) = 3x + 4\).

**Tip:** Always distribute negative signs carefully, as they can change the signs of terms inside parentheses.

Learn how to solve the linear equation 4x - (x - 4) = 5x + 3(x - 35) using algebraic techniques, including the distributive property and simplification. This step-by-step solution is suitable for students in Grades 8-10.

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