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The problem asks to solve for \( m \) in two inequalities:

\[
\frac{5m - 3}{2} < 6 \quad \text{or} \quad \frac{3m + 5}{4} > 5
\]

### Solving the first inequality:

\[
\frac{5m - 3}{2} < 6
\]

1. Multiply both sides by 2 to eliminate the denominator:
   \[
   5m - 3 < 12
   \]

2. Add 3 to both sides:
   \[
   5m < 15
   \]

3. Divide by 5:
   \[
   m < 3
   \]

### Solving the second inequality:

\[
\frac{3m + 5}{4} > 5
\]

1. Multiply both sides by 4 to eliminate the denominator:
   \[
   3m + 5 > 20
   \]

2. Subtract 5 from both sides:
   \[
   3m > 15
   \]

3. Divide by 3:
   \[
   m > 5
   \]

### Combined solution:

- From the first inequality: \( m < 3 \)
- From the second inequality: \( m > 5 \)

This results in no overlap, so the solution is:
- \( m < 3 \) or \( m > 5 \).

### Graphing the solution:

On a number line, this means two rays:
- One extending left from 3 (open circle at 3),
- One extending right from 5 (open circle at 5).

Would you like further clarification or details? Here are five related questions:

1. How do we handle "or" conditions in inequalities?
2. What is the difference between strict and non-strict inequalities?
3. How do we solve compound inequalities with "and"?
4. What changes if the inequality symbols are "≤" or "≥"?
5. How do we check if the inequality solution is correct?

**Tip:** Always double-check the inequality direction when multiplying or dividing by a negative number—it reverses the inequality sign!

Solve for m and graph the solution. The inequalities are (5m - 3)/2 < 6 or (3m + 5)/4 > 5.

Learn how to solve and graph inequalities such as (5m - 3)/2 < 6 or (3m + 5)/4 > 5. The step-by-step solution involves solving two separate inequalities and graphing the final result on a number line. Suitable for Grades 7-10.

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