1. **State the problem:** Solve the equation $$2(3x - 5) + 4 = 3(x + 2) - 1$$. 2. **Use the distributive property:** Multiply terms inside parentheses. $$2 \times 3x = 6x$$ $$2 \times (-5) = -10$$ So the equation becomes: $$6x - 10 + 4 = 3x + 6 - 1$$ 3. **Simplify both sides:** Combine like terms. Left side: $$-10 + 4 = -6$$ Right side: $$6 - 1 = 5$$ So the equation is: $$6x - 6 = 3x + 5$$ 4. **Isolate variable terms on one side:** Subtract $$3x$$ from both sides. $$6x - 6 - 3x = 3x + 5 - 3x$$ Intermediate step with cancellation: $$\cancel{6x} - 6 - \cancel{3x} = \cancel{3x} + 5 - \cancel{3x}$$ Simplifies to: $$3x - 6 = 5$$ 5. **Isolate the constant term:** Add 6 to both sides. $$3x - 6 + 6 = 5 + 6$$ Intermediate step: $$3x - \cancel{6} + \cancel{6} = 11$$ Simplifies to: $$3x = 11$$ 6. **Solve for $$x$$:** Divide both sides by 3. $$\frac{3x}{3} = \frac{11}{3}$$ Intermediate step with cancellation: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{11}{3}$$ Simplifies to: $$x = \frac{11}{3}$$ **Final answer:** $$x = \frac{11}{3}$$