1. **State the problem:** Solve the equation $$7x - 2 \times \{4 \times (2x - 7) - 5 \times [2 - 3 \times (x + 2) + 1]\} = 3 \times (5 - 13x)$$. 2. **Apply the distributive property and simplify inside the brackets:** Inside the square brackets: $$2 - 3 \times (x + 2) + 1 = 2 - 3x - 6 + 1 = (2 + 1 - 6) - 3x = -3 - 3x$$ 3. **Substitute back and simplify the curly braces:** $$4 \times (2x - 7) - 5 \times [-3 - 3x] = 8x - 28 + 15 + 15x = (8x + 15x) + (-28 + 15) = 23x - 13$$ 4. **Rewrite the original equation:** $$7x - 2 \times (23x - 13) = 3 \times (5 - 13x)$$ 5. **Distribute the -2:** $$7x - 46x + 26 = 15 - 39x$$ 6. **Combine like terms on the left:** $$-39x + 26 = 15 - 39x$$ 7. **Add $39x$ to both sides:** $$-39x + 26 + 39x = 15 - 39x + 39x$$ $$\cancel{-39x} + 26 + \cancel{39x} = 15 + \cancel{-39x} + \cancel{39x}$$ $$26 = 15$$ 8. **Analyze the result:** The statement $26 = 15$ is false, which means there is no solution to the equation. **Final answer:** The equation has \textbf{no solution}.