We are given the equation:

\[
\frac{m+1}{4} + \frac{5}{6} = \frac{2m-1}{12}
\]

To solve this, we need to eliminate the denominators by finding the least common denominator (LCD). The denominators are 4, 6, and 12, and the LCD is 12. 

Let's multiply every term in the equation by 12 to eliminate the fractions:

\[
12 \times \left( \frac{m+1}{4} \right) + 12 \times \left( \frac{5}{6} \right) = 12 \times \left( \frac{2m-1}{12} \right)
\]

Simplifying each term:

\[
3(m+1) + 2(5) = 2m - 1
\]

Now expand:

\[
3m + 3 + 10 = 2m - 1
\]

Simplify the left-hand side:

\[
3m + 13 = 2m - 1
\]

Now, let's move all the terms involving \( m \) to one side and constants to the other side:

\[
3m - 2m = -1 - 13
\]

Simplifying:

\[
m = -14
\]

Thus, the solution is:

\[
m = -14
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions to practice:
1. Solve: \(\frac{2x+3}{5} + \frac{7}{3} = \frac{x-1}{15}\)
2. Simplify: \(\frac{3}{4} + \frac{5}{6} - \frac{1}{12}\)
3. Solve for \(x\): \(\frac{x+2}{3} - \frac{1}{4} = \frac{5x+1}{12}\)
4. Solve: \(\frac{m+2}{5} + \frac{4}{3} = \frac{3m+7}{15}\)
5. Solve for \(y\): \( \frac{2y+1}{6} = \frac{y-3}{3} \)

**Tip:** Always try to eliminate fractions early by multiplying through by the least common denominator (LCD).

Learn how to solve the linear equation (m+1)/4 + 5/6 = (2m-1)/12 by finding the least common denominator and simplifying the equation. This step-by-step solution involves key algebraic concepts like linear equations and working with fractions. Suitable for students in Grades 7-9.

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