To solve the limit

$\lim_{x \to 3} \frac{6x - 3}{2x - 4},$

we can evaluate it step by step:

Step 1: Direct Substitution

Substitute $x = 3$ directly into the expression:

$\frac{6(3) - 3}{2(3) - 4} = \frac{18 - 3}{6 - 4} = \frac{15}{2}.$

Final Answer:

$\lim_{x \to 3} \frac{6x - 3}{2x - 4} = \frac{15}{2}.$

Would you like further details, or have any questions?

Here are 5 related questions for further exploration:

1. What is the concept of a limit in calculus?
2. How do you handle limits where direct substitution leads to an indeterminate form?
3. What techniques can be used for limits involving fractions and polynomials?
4. How does L'Hôpital's rule apply to limits of the form $\frac{0}{0}$?
5. What is the difference between one-sided and two-sided limits?

Tip: Always try direct substitution first when calculating limits; if that fails, consider algebraic simplifications or special techniques like factoring or L'Hôpital's rule.