1. **State the problem:** Simplify the expression $$\{[8x-5+(2x-3)]-[-4x+7-(x+2)]\}$$ and find the result. 2. **Rewrite the expression by removing brackets carefully:** $$[8x - 5 + (2x - 3)] - [-4x + 7 - (x + 2)]$$ 3. **Simplify inside the first bracket:** $$8x - 5 + 2x - 3 = (8x + 2x) + (-5 - 3) = 10x - 8$$ 4. **Simplify inside the second bracket:** Inside the second bracket we have: $$-4x + 7 - (x + 2) = -4x + 7 - x - 2 = (-4x - x) + (7 - 2) = -5x + 5$$ 5. **Now the expression becomes:** $$[10x - 8] - [-5x + 5]$$ 6. **Remove the minus sign before the second bracket by distributing the minus:** $$10x - 8 + 5x - 5$$ 7. **Combine like terms:** $$10x + 5x = 15x$$ $$-8 - 5 = -13$$ 8. **Final simplified expression:** $$\boxed{15x - 13}$$ **Explanation:** We carefully removed brackets and distributed minus signs, then combined like terms to simplify the expression step-by-step.