1. **State the problem:** Solve for $Y$ in the equation $$\frac{50 - 1.75Y}{1.5} = x.$$\n\n2. **Isolate the numerator:** Multiply both sides by 1.5 to eliminate the denominator:\n$$\cancel{1.5} \times \frac{50 - 1.75Y}{\cancel{1.5}} = 1.5x \implies 50 - 1.75Y = 1.5x.$$\n\n3. **Isolate the term with $Y$:** Subtract 50 from both sides:\n$$50 - 1.75Y - 50 = 1.5x - 50 \implies -1.75Y = 1.5x - 50.$$\n\n4. **Solve for $Y$:** Divide both sides by $-1.75$:\n$$Y = \frac{1.5x - 50}{-1.75} = \frac{\cancel{1.5}x - 50}{\cancel{-1.75}}.$$\n\n5. **Simplify the fraction:**\n$$Y = -\frac{1.5x - 50}{1.75} = -\frac{1.5x}{1.75} + \frac{50}{1.75}.$$\n\n6. **Express as decimals or simplified fractions:**\n$$Y = -\frac{6}{7}x + \frac{200}{7}.$$\n\n**Final answer:** $$Y = -\frac{6}{7}x + \frac{200}{7}.$$