1. **State the problem:** Solve the equation $8(x-3)-2(3-x)=2(x+2)-5(5-x)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$8(x-3) = 8x - 24$$ $$-2(3-x) = -2 \times 3 + 2x = -6 + 2x$$ $$2(x+2) = 2x + 4$$ $$-5(5-x) = -25 + 5x$$ 3. **Rewrite the equation with distributed terms:** $$8x - 24 - 6 + 2x = 2x + 4 - 25 + 5x$$ 4. **Combine like terms on each side:** Left side: $8x + 2x - 24 - 6 = 10x - 30$ Right side: $2x + 5x + 4 - 25 = 7x - 21$ So the equation becomes: $$10x - 30 = 7x - 21$$ 5. **Isolate variable terms on one side and constants on the other:** Subtract $7x$ from both sides: $$10x - \cancel{7x} - 30 = \cancel{7x} - 21$$ $$3x - 30 = -21$$ 6. **Add 30 to both sides to isolate the term with $x$:** $$3x - 30 + 30 = -21 + 30$$ $$3x = 9$$ 7. **Divide both sides by 3 to solve for $x$:** $$\frac{3x}{\cancel{3}} = \frac{9}{\cancel{3}}$$ $$x = 3$$ **Final answer:** $x = 3$