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The equation you provided is:

\[
-2(-4v + 9) - 9v = 5(v - 4) - 8
\]

Let's solve for \( v \).

### Step 1: Expand both sides of the equation
First, distribute the multiplication on both sides:

\[
-2(-4v + 9) = 8v - 18
\]
\[
5(v - 4) = 5v - 20
\]

Now substitute these into the equation:

\[
(8v - 18) - 9v = (5v - 20) - 8
\]

### Step 2: Simplify both sides
Combine like terms:

On the left:
\[
8v - 9v - 18 = -v - 18
\]

On the right:
\[
5v - 20 - 8 = 5v - 28
\]

So the equation becomes:
\[
-v - 18 = 5v - 28
\]

### Step 3: Solve for \( v \)
Add \( v \) to both sides:
\[
-18 = 6v - 28
\]

Now add 28 to both sides:
\[
10 = 6v
\]

Finally, divide by 6:
\[
v = \frac{10}{6} = \frac{5}{3}
\]

Thus, the solution is:
\[
v = \frac{5}{3}
\]

Would you like more details on any step or further explanation?

Here are some related problems you might find useful:
1. Solve \( 2(-3x + 5) - 7x = 3(x + 2) - 10 \).
2. Simplify and solve: \( -5(2y - 4) + 3y = 6(2y - 3) \).
3. Solve the linear equation: \( 4(3 - x) - 2(x + 1) = 5(x - 4) + 3 \).
4. Solve the equation with fractions: \( \frac{2x - 5}{3} + 4 = \frac{x}{2} \).
5. Find the value of \( x \) for: \( 3(x + 4) - 2x = 5x + 9 \).

**Tip:** Always combine like terms and simplify expressions step by step to avoid errors!

Solve for v: -2(-4v + 9) - 9v = 5(v - 4) - 8

Learn how to solve the linear equation -2(-4v + 9) - 9v = 5(v - 4) - 8 with detailed steps. This problem involves the distributive property and simplification of linear terms, suitable for students in Grades 8-10.

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