1. **State the problem:** Solve the equation $$3^{0}(2x - 5) + (-x - 5) = -3(x^{0} - 2)$$. 2. **Recall important rules:** - Any number raised to the zero power is 1, so $$3^{0} = 1$$ and $$x^{0} = 1$$. - Distribute multiplication over addition/subtraction. 3. **Rewrite the equation using these rules:** $$1 \times (2x - 5) + (-x - 5) = -3 \times (1 - 2)$$ 4. **Simplify both sides:** Left side: $$2x - 5 - x - 5 = (2x - x) + (-5 - 5) = x - 10$$ Right side: $$-3 \times (-1) = 3$$ 5. **Set up the simplified equation:** $$x - 10 = 3$$ 6. **Solve for $$x$$:** Add 10 to both sides: $$x - 10 + 10 = 3 + 10$$ $$x = 13$$ **Final answer:** $$x = 13$$