We are given the equation:

\[
\frac{15}{8}m - 11 = \frac{7}{4}m + 1
\]

To solve for \(m\), follow these steps:

### Step 1: Eliminate fractions
To get rid of the fractions, find the least common denominator (LCD) of 8 and 4, which is 8. Multiply both sides of the equation by 8:

\[
8 \times \left( \frac{15}{8}m - 11 \right) = 8 \times \left( \frac{7}{4}m + 1 \right)
\]

This simplifies to:

\[
15m - 88 = 14m + 8
\]

### Step 2: Move all terms involving \(m\) to one side
Subtract \(14m\) from both sides:

\[
15m - 14m - 88 = 8
\]

Simplifying gives:

\[
m - 88 = 8
\]

### Step 3: Solve for \(m\)
Add 88 to both sides:

\[
m = 96
\]

Thus, the solution is:

\[
m = 96
\]

Would you like more details or have any questions?

### Related questions:
1. How do you handle equations with variables on both sides?
2. Can you show another example of solving an equation with fractions?
3. How can we check the solution \(m = 96\)?
4. What if the equation had a higher degree (e.g., quadratic)?
5. How do you simplify complex fractions in equations?

**Tip:** Always check your final solution by plugging it back into the original equation!

Learn how to solve the linear equation with fractions, 15/8m - 11 = 7/4m + 1, using step-by-step techniques such as eliminating fractions by multiplying by the least common denominator (LCD). This solution is perfect for students in Grades 8-10 and covers key algebra concepts.

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