To evaluate the limit of the expression \(\lim_{x \to 3} \frac{5x + 2}{2x - 3}\), we follow these steps:

### Step 1: Direct Substitution
First, attempt to substitute \(x = 3\) directly into the expression:

\[
\frac{5(3) + 2}{2(3) - 3} = \frac{15 + 2}{6 - 3} = \frac{17}{3}
\]

### Conclusion:
The limit as \(x\) approaches 3 is:

\[
\lim_{x \to 3} \frac{5x + 2}{2x - 3} = \frac{17}{3}
\]

Would you like further details on any of the steps, or do you have any questions?

### Related Questions:
1. What happens if the denominator approaches zero in similar limits?
2. How would the limit change if \(x\) approaches a value other than 3?
3. What is the difference between evaluating limits at a point and at infinity?
4. Can you provide examples of limits that result in indeterminate forms like \(0/0\)?
5. How do we handle limits where the function has a discontinuity?

**Tip**: Always try direct substitution first when evaluating limits; if that leads to an indeterminate form, then explore algebraic simplifications or other techniques.

Explore the limit calculation of the expression (5x + 2) / (2x - 3) as x approaches 3. This problem focuses on key concepts in limits and algebra, applying direct substitution to find the value of the limit. Ideal for students in Grades 10-12.

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