The equation you provided is:

\[
b + 1 = \frac{1}{4}(3b + 2)
\]

Let's solve it step by step:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 4 to eliminate the fraction on the right-hand side:

\[
4(b + 1) = 3b + 2
\]

### Step 2: Distribute the 4 on the left-hand side
\[
4b + 4 = 3b + 2
\]

### Step 3: Move all terms involving \( b \) to one side
Subtract \( 3b \) from both sides:

\[
4b - 3b + 4 = 2
\]

This simplifies to:

\[
b + 4 = 2
\]

### Step 4: Solve for \( b \)
Subtract 4 from both sides:

\[
b = 2 - 4
\]

\[
b = -2
\]

Thus, the solution is \( b = -2 \).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would the equation change if there were different coefficients for \( b \)?
2. What happens if the constant term on the right-hand side is larger?
3. How can this method be applied to equations with more variables?
4. Can you solve a similar equation with a different fractional coefficient?
5. What if the fraction were negative instead?

**Tip:** Always eliminate fractions first to simplify the solving process.

This detailed solution walks through the steps to solve the linear equation b + 1 = 1/4(3b + 2). Learn how to eliminate fractions, distribute terms, and solve for variables. Suitable for students in Grades 6-8, this example emphasizes foundational algebraic concepts.

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