1. **State the problem:** Solve the equation $3(x-2)-(4x-5)=2$ for $x$. 2. **Write down the equation:** $$3(x-2)-(4x-5)=2$$ 3. **Apply the distributive property:** $$3 \times x - 3 \times 2 - 4x + 5 = 2$$ which simplifies to $$3x - 6 - 4x + 5 = 2$$ 4. **Combine like terms:** $$3x - 4x - 6 + 5 = 2$$ $$-x - 1 = 2$$ 5. **Isolate the variable $x$:** Add 1 to both sides: $$-x = 2 + 1$$ $$-x = 3$$ 6. **Solve for $x$:** Multiply both sides by $-1$: $$x = -3$$ **Final answer:** $$x = -3$$