Solve by graphing: $$ \frac{3 x}{2 x-1}=2 x-3 $$ $$ \left\{-\frac{7}{20}, \frac{21}{10}\right\} $$ $$ \left\{-1, \frac{3}{4}\right\} $$ $$ \left\{\frac{3}{10}\right\} $$ $$ \left\{\frac{3}{10}, \frac{12}{5}\right\} $$

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To solve the equation $$ \frac{3x}{2x - 1} = 2x - 3 $$ by graphing, we'll follow these steps:

1. **Understand the Equation:**
   - **Left Side (Function 1):** $$ y = \frac{3x}{2x - 1} $$
   - **Right Side (Function 2):** $$ y = 2x - 3 $$

By graphing these two functions, the solutions to the equation will be the $$ x $$-values where the graphs intersect.

2. **Algebraic Solution (for Verification):**
   
   While graphing provides a visual solution, solving algebraically ensures accuracy.

$$
   \frac{3x}{2x - 1} = 2x - 3
   $$
   
   **Step-by-Step:**
   
   - **Multiply both sides by $$ 2x - 1 $$ to eliminate the fraction:**
     $$
     3x = (2x - 3)(2x - 1)
     $$
   
   - **Expand the right side:**
     $$
     3x = 4x^2 - 8x + 3
     $$
   
   - **Rearrange to form a quadratic equation:**
     $$
     4x^2 - 11x + 3 = 0
     $$
   
   - **Solve using the quadratic formula $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$:**
     $$
     x = \frac{11 \pm \sqrt{121 - 48}}{8} = \frac{11 \pm \sqrt{73}}{8}
     $$
     
     - **Approximate Solutions:**
       $$
       x \approx \frac{11 + 8.544}{8} \approx 2.443 \quad \text{and} \quad x \approx \frac{11 - 8.544}{8} \approx 0.307
       $$
   
   - **Solutions:**
     $$
     x \approx 0.307 \quad \text{and} \quad x \approx 2.443
     $$

3. **Matching with Provided Options:**

The approximate solutions $$ 0.307 $$ and $$ 2.443 $$ correspond closely to the fractions $$ \frac{3}{10} $$ and $$ \frac{12}{5} $$ respectively.

**Given Options:**
   - $$ \left\{-\frac{7}{20}, \frac{21}{10}\right\} = \{-0.35, 2.1\} $$
   - $$ \left\{-1, \frac{3}{4}\right\} = \{-1, 0.75\} $$
   - $$ \left\{\frac{3}{10}\right\} = \{0.3\} $$
   - $$ \left\{\frac{3}{10}, \frac{12}{5}\right\} = \{0.3, 2.4\} $$

**Conclusion:**
   
   The correct solutions are $$ \frac{3}{10} $$ and $$ \frac{12}{5} $$.

**Answer:**
   $$
   \boxed{\left\{\dfrac{3}{10},\, \dfrac{12}{5}\right\}}
   $$
The solutions are $$ x = \frac{3}{10} $$ and $$ x = \frac{12}{5} $$.

Solve by graphing:

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