1. **State the problem:** Solve the equation $$\frac{7}{12}x + \frac{10x - 15}{3} - x = \frac{4(2x - 1)}{3} - \frac{3(2 - x)}{4}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side to find its value. 3. **Find a common denominator:** The denominators are 12, 3, and 4. The least common denominator (LCD) is 12. 4. **Multiply every term by 12 to clear denominators:** $$12 \times \left(\frac{7}{12}x\right) + 12 \times \left(\frac{10x - 15}{3}\right) - 12 \times x = 12 \times \left(\frac{4(2x - 1)}{3}\right) - 12 \times \left(\frac{3(2 - x)}{4}\right)$$ 5. **Simplify each term:** $$7x + 4(10x - 15) - 12x = 4 \times 4(2x - 1) - 3 \times 3(2 - x)$$ 6. **Calculate the multiplications:** $$7x + 40x - 60 - 12x = 16x - 4 - 9(2 - x)$$ 7. **Simplify left side:** $$ (7x + 40x - 12x) - 60 = 16x - 4 - 9(2 - x)$$ $$35x - 60 = 16x - 4 - 9(2 - x)$$ 8. **Distribute on right side:** $$35x - 60 = 16x - 4 - 18 + 9x$$ 9. **Combine like terms on right side:** $$35x - 60 = (16x + 9x) - (4 + 18)$$ $$35x - 60 = 25x - 22$$ 10. **Bring all $x$ terms to one side and constants to the other:** $$35x - 25x = -22 + 60$$ $$10x = 38$$ 11. **Divide both sides by 10:** $$x = \frac{\cancel{10}x}{\cancel{10}} = \frac{38}{10}$$ 12. **Simplify the fraction:** $$x = \frac{19}{5}$$ **Final answer:** $$x = \frac{19}{5}$$