1. **State the problem:** Solve the first equation given: $$50x \cdot 7 + 3 = 3x - \frac{5x}{4}$$ 2. **Rewrite the equation:** Multiply and simplify terms: $$350x + 3 = 3x - \frac{5x}{4}$$ 3. **Bring all terms involving $x$ to one side:** $$350x - 3x + \frac{5x}{4} = -3$$ 4. **Find common denominator and combine $x$ terms:** $$\left(350 - 3 + \frac{5}{4}\right)x = -3$$ $$\left(347 + \frac{5}{4}\right)x = -3$$ $$\frac{(347 \times 4) + 5}{4} x = -3$$ $$\frac{1388 + 5}{4} x = -3$$ $$\frac{1393}{4} x = -3$$ 5. **Solve for $x$ by dividing both sides:** $$x = \frac{-3}{\frac{1393}{4}} = -3 \times \frac{4}{1393} = -\frac{12}{1393}$$ 6. **Final answer:** $$x = -\frac{12}{1393}$$ This completes the solution for the first equation.