We have the equation:

\[
\frac{2}{3} + \frac{3m}{5} = \frac{31}{15}
\]

### Step 1: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD) of the denominators 3, 5, and 15, which is 15.

### Step 2: Multiply every term by 15
Multiplying each term by 15 gives:

\[
15 \times \frac{2}{3} + 15 \times \frac{3m}{5} = 15 \times \frac{31}{15}
\]

Simplifying each term:

\[
5 \times 2 + 3 \times 3m = 31
\]

This simplifies to:

\[
10 + 9m = 31
\]

### Step 3: Solve for \( m \)
Subtract 10 from both sides:

\[
9m = 21
\]

Now, divide both sides by 9:

\[
m = \frac{21}{9} = \frac{7}{3}
\]

### Final Answer:
\[
m = \frac{7}{3}
\]

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

Here are 5 related questions to explore further:
1. How do you solve equations with variables on both sides?
2. How do you find the least common denominator of fractions?
3. What is the process for solving linear equations with fractions?
4. How do you convert improper fractions to mixed numbers?
5. How do you check if your solution to an equation is correct?

**Tip:** When working with fractions in equations, multiplying through by the least common denominator can simplify the problem quickly.

This guide provides a step-by-step solution to the linear equation 2/3 + 3m/5 = 31/15. Learn how to eliminate fractions using the least common denominator and solve for the variable. Ideal for students in Grades 6-8.

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