Let's solve the equation step by step:

\[
\frac{5}{4}m + 1 + 4 = \frac{15}{2}
\]

### Step 1: Simplify the constants on the left side
Combine the constants \(1 + 4 = 5\):

\[
\frac{5}{4}m + 5 = \frac{15}{2}
\]

### Step 2: Subtract 5 from both sides
To isolate the term with \(m\), subtract 5 from both sides:

\[
\frac{5}{4}m = \frac{15}{2} - 5
\]

### Step 3: Simplify the right side
First, express 5 as a fraction with a denominator of 2:

\[
5 = \frac{10}{2}
\]

Now subtract:

\[
\frac{5}{4}m = \frac{15}{2} - \frac{10}{2} = \frac{5}{2}
\]

### Step 4: Solve for \(m\)
To isolate \(m\), multiply both sides by the reciprocal of \(\frac{5}{4}\), which is \(\frac{4}{5}\):

\[
m = \frac{5}{2} \times \frac{4}{5} = \frac{5 \times 4}{2 \times 5} = \frac{20}{10} = 2
\]

### Final answer:
\[
m = 2
\]

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

Here are 5 related questions:
1. How would you solve \( \frac{7}{3}m + 2 = \frac{19}{6} \)?
2. How can you simplify fractional equations with different denominators?
3. What is the general method for solving linear equations involving fractions?
4. What is the inverse operation of multiplying by a fraction in equations?
5. How can you check if your solution to a fractional equation is correct?

**Tip:** When solving equations with fractions, clear the fractions early by multiplying by the least common denominator (LCD).

Learn how to solve the linear equation 5/4m + 1 + 4 = 15/2 with a step-by-step solution. This problem includes key algebraic concepts, focusing on operations with fractions and solving linear equations. Suitable for students in Grades 6-8.

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