1. **State the problem:** We have a rectangular garden with length $x + 2$ meters and width $x - 3$ meters. There is a walkway of width 1 meter surrounding the garden on all sides. We need to find an expression for the area of the walkway alone and simplify it. 2. **Understand the problem:** The walkway surrounds the garden, so the total length and width including the walkway will be increased by 2 meters (1 meter on each side). 3. **Write expressions for total dimensions including walkway:** - Total length = $(x + 2) + 2 = x + 4$ - Total width = $(x - 3) + 2 = x - 1$ 4. **Write expressions for areas:** - Area of garden = length $\times$ width = $(x + 2)(x - 3)$ - Area of garden plus walkway = total length $\times$ total width = $(x + 4)(x - 1)$ 5. **Area of walkway alone:** $$\text{Area of walkway} = \text{Area of garden plus walkway} - \text{Area of garden}$$ 6. **Expand both areas:** - Expand garden area: $$ (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6 $$ - Expand total area: $$ (x + 4)(x - 1) = x^2 - x + 4x - 4 = x^2 + 3x - 4 $$ 7. **Subtract to find walkway area:** $$ (x^2 + 3x - 4) - (x^2 - x - 6) = x^2 + 3x - 4 - x^2 + x + 6 = 4x + 2 $$ 8. **Final simplified expression:** $$\boxed{4x + 2}$$ This expression represents the area of the walkway alone in terms of $x$ meters. **Summary:** The area of the walkway alone is $4x + 2$ square meters.