Let's solve the equation step by step:

### Given:
\[
10x - (5x - 10) = -( -4x + 8 ) - 3
\]

#### Step 1: Simplify both sides.

**Left side:**
Distribute the negative sign:
\[
10x - 5x + 10
\]
Simplify:
\[
5x + 10
\]

**Right side:**
Distribute the negative sign:
\[
4x - 8 - 3
\]
Simplify:
\[
4x - 11
\]

So now the equation becomes:
\[
5x + 10 = 4x - 11
\]

#### Step 2: Move variables and constants to one side.

Subtract \(4x\) from both sides:
\[
5x - 4x + 10 = -11
\]
Simplify:
\[
x + 10 = -11
\]

Subtract 10 from both sides:
\[
x = -11 - 10
\]
Simplify:
\[
x = -21
\]

### Solution:
\[
x = -21
\]

Would you like more details or have any questions?

Here are some related questions to practice:
1. Solve \(7x - (3x - 6) = -(5x - 9)\).
2. Solve \(12x + (4 - 3x) = 2x - 8\).
3. Simplify and solve \(2(x + 4) - 3 = 5 - (x - 2)\).
4. Solve \(6x - (2x + 5) = -(x - 10) + 7\).
5. Solve \(8x - 3(2x - 5) = -(4x + 2) + 9\).

**Tip:** Always distribute negative signs carefully, as they can change the entire expression.

Learn how to solve the linear equation 10x - (5x - 10) = -( -4x + 8 ) - 3 step by step. This problem involves the distributive property and equation simplification, making it suitable for students in Grades 8-10.

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