Let's solve the equation:

\[
-( -10x + 1 ) - 4x = 7x
\]

### Step 1: Distribute the negative sign.
\[
-(-10x + 1) = 10x - 1
\]
So the equation becomes:
\[
10x - 1 - 4x = 7x
\]

### Step 2: Combine like terms on the left-hand side.
\[
(10x - 4x) - 1 = 7x
\]
This simplifies to:
\[
6x - 1 = 7x
\]

### Step 3: Move all terms involving \(x\) to one side.
Subtract \(6x\) from both sides:
\[
-1 = 7x - 6x
\]
\[
-1 = x
\]

### Final Answer:
\[
x = -1
\]

Let me know if you need more details or have any questions.

Here are 5 related questions for practice:
1. Solve: \( -(3x - 5) + 2x = 6x \)
2. Simplify: \( -(-8x + 4) - 5x = 10x \)
3. Solve: \( 2x - (5x + 3) = -4x + 7 \)
4. Solve for \(x\): \( 3x - 7 - (2x - 4) = 5x \)
5. Solve: \( -(2x - 9) + 4 = 3x \)

**Tip:** Always be careful when distributing negative signs across parentheses to avoid sign errors.

Learn how to solve the linear equation −(−10x+1)−4x=7x with a detailed step-by-step solution. This problem covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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