To solve the equation:

\[
-\frac{2}{3}(-8x + 2) - 1 = 10x + 2x - 3
\]

### Step 1: Distribute \(-\frac{2}{3}\) across \(-8x + 2\)
\[
-\frac{2}{3} \times -8x = \frac{16x}{3}
\]
\[
-\frac{2}{3} \times 2 = -\frac{4}{3}
\]
Now the equation becomes:
\[
\frac{16x}{3} - \frac{4}{3} - 1 = 10x + 2x - 3
\]

### Step 2: Simplify the left and right-hand sides
On the left side, combine \(-\frac{4}{3} - 1\):
\[
-\frac{4}{3} - 1 = -\frac{4}{3} - \frac{3}{3} = -\frac{7}{3}
\]
So the equation becomes:
\[
\frac{16x}{3} - \frac{7}{3} = 12x - 3
\]

### Step 3: Eliminate fractions by multiplying through by 3
Multiply both sides of the equation by 3 to eliminate the denominators:
\[
16x - 7 = 3(12x - 3)
\]
Distribute the 3 on the right-hand side:
\[
16x - 7 = 36x - 9
\]

### Step 4: Solve for \(x\)
Move all terms involving \(x\) to one side and constants to the other:
\[
16x - 36x = -9 + 7
\]
Simplify both sides:
\[
-20x = -2
\]

### Step 5: Solve for \(x\)
\[
x = \frac{-2}{-20} = \frac{1}{10}
\]

### Final Answer:
\[
x = \frac{1}{10}
\]

Would you like more details on any step? 

Here are some follow-up questions:
1. How do you handle equations with fractions?
2. What is the distributive property, and how is it used in equations?
3. How do you clear fractions in an equation?
4. What are the steps to isolate \(x\) in a linear equation?
5. What happens when the variable cancels out on both sides?

**Tip:** Always simplify the equation step-by-step to avoid errors when dealing with fractions.

Learn how to solve the linear equation (-2/3)(-8x + 2) - 1 = 12x - 3 step-by-step using the distributive property and fraction elimination. This problem covers key algebra concepts and is suitable for students in Grades 8-10.

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