Let's solve the equation step by step:

The equation is:

\[
-4(3w + 10) = 9 - 6w + w
\]

### Step 1: Distribute the \(-4\) on the left side of the equation.
\[
-12w - 40 = 9 - 5w
\]

### Step 2: Move all terms involving \(w\) to one side of the equation and constant terms to the other side.
Add \(12w\) to both sides:
\[
-40 = 9 + 7w
\]

### Step 3: Isolate the variable term.
Subtract \(9\) from both sides:
\[
-49 = 7w
\]

### Step 4: Solve for \(w\) by dividing both sides by \(7\):
\[
w = \frac{-49}{7} = -7
\]

So, the solution is \( w = -7 \).

Would you like to go into more detail or have any questions?

Here are 5 related questions for further practice:

1. Solve: \( 2(5x + 3) = 4x - 7 \).
2. Solve: \( -3(2y - 4) = 8 + 5y \).
3. Solve: \( 6(z - 2) = 12z + 4 \).
4. Solve: \( -2(4m + 9) = 7m + 3 \).
5. Solve: \( 5(3n - 2) = 2n + 14 \).

**Tip:** When distributing a negative number across a binomial, ensure each term inside the parentheses changes its sign.

Learn how to solve the equation -4(3w + 10) = 9 - 6w + w with a detailed step-by-step solution. This problem involves linear equations and the distributive property. Suitable for students in Grades 7-9.

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