1. **State the problem:** We are given the equation $$2(2x - 2) = 3x - 7$$ which relates the height of a door and the length of a garland. 2. **Write the equation and expand:** Use the distributive property to expand the left side: $$2(2x - 2) = 4x - 4$$ So the equation becomes: $$4x - 4 = 3x - 7$$ 3. **Isolate the variable:** Subtract $$3x$$ from both sides: $$4x - 3x - 4 = -7$$ Simplify: $$x - 4 = -7$$ 4. **Solve for $$x$$:** Add 4 to both sides: $$x = -7 + 4$$ $$x = -3$$ 5. **Find the height of the door:** Substitute $$x = -3$$ into $$2x - 2$$: $$2(-3) - 2 = -6 - 2 = -8$$ feet 6. **Find the length of the garland:** Substitute $$x = -3$$ into $$3x - 7$$: $$3(-3) - 7 = -9 - 7 = -16$$ feet **Note:** The negative values for height and length indicate that the solution $$x = -3$$ may not be physically meaningful in this context, as lengths cannot be negative. **Final answer:** $$x = -3$$, height = $$-8$$ ft, garland length = $$-16$$ ft (not physically valid).