To solve the equation:

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

### Step 1: Eliminate the fractions
Multiply the entire equation by 4, the least common denominator (LCD) of 4 and 2, to eliminate the fractions:

\[
4 \times \left(\frac{1}{4}b + 1\right) = 4 \times \left(-\frac{1}{2}b + 3\right)
\]

This gives:

\[
b + 4 = -2b + 12
\]

### Step 2: Move all terms involving \(b\) to one side
Add \(2b\) to both sides:

\[
b + 2b + 4 = 12
\]

Simplifying:

\[
3b + 4 = 12
\]

### Step 3: Isolate \(b\)
Subtract 4 from both sides:

\[
3b = 8
\]

### Step 4: Solve for \(b\)
Divide both sides by 3:

\[
b = \frac{8}{3}
\]

Thus, the solution is:

\[
b = \frac{8}{3}
\]

Would you like further details or explanations? 

Here are 5 related questions to expand your understanding:

1. What are some other methods for solving equations with fractions?
2. How can we check if the solution \(b = \frac{8}{3}\) is correct?
3. What happens if both sides of an equation have fractions with different denominators?
4. Can we solve this equation using substitution?
5. What strategies can simplify solving equations with more complex fractions?

**Tip:** Always check your solution by substituting it back into the original equation to verify correctness.

This tutorial shows how to solve the linear equation \frac{1}{4}b + 1 = -\frac{1}{2}b + 3 using fraction elimination and variable isolation. Suitable for students in Grades 7-8, this problem introduces solving linear equations with fractions and provides a clear step-by-step solution.

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