Let's solve the equation step by step:

\[
-2(1 - 6b) + b = 38 + 8b
\]

### Step 1: Distribute the \(-2\) to the terms inside the parentheses.
\[
-2(1) + (-2)(-6b) + b = 38 + 8b
\]
\[
-2 + 12b + b = 38 + 8b
\]

### Step 2: Combine like terms on the left-hand side.
\[
-2 + 13b = 38 + 8b
\]

### Step 3: Move all terms involving \(b\) to one side and constants to the other side. Subtract \(8b\) from both sides:
\[
-2 + 13b - 8b = 38
\]
\[
-2 + 5b = 38
\]

### Step 4: Add 2 to both sides to isolate the term with \(b\):
\[
5b = 40
\]

### Step 5: Divide by 5 to solve for \(b\):
\[
b = \frac{40}{5} = 8
\]

Thus, the solution is:
\[
b = 8
\]

Would you like a detailed explanation of any of the steps, or have any other questions?

Here are 5 related questions for further practice:
1. Solve \( 3(2 - 5x) + 4x = 7x - 15 \).
2. What is the solution to \( 5(1 - 3p) + 2p = 4p + 30 \)?
3. If \( 6(2x + 1) - x = 12 + 7x \), what is \(x\)?
4. Solve the equation \( 4a - 3(2a - 5) = 7 + a \).
5. What is the solution to \( 9 - 2y = 7 + 4y \)?

**Tip:** Always combine like terms before moving variables to one side of the equation. This simplifies your work significantly!

Learn how to solve the linear equation -2(1 - 6b) + b = 38 + 8b step by step. This problem involves key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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