1. **Problem 22:** Given a rectangle with length $x + 4$ and width $x - 2$, we need to: a) Write the expression for the perimeter. b) Find the perimeter when $x = 5$. 2. **Formula for perimeter of a rectangle:** The perimeter $P$ of a rectangle is given by: $$P = 2(\text{length} + \text{width})$$ 3. **Step a) Write the expression:** Substitute length and width: $$P = 2((x + 4) + (x - 2))$$ Simplify inside the parentheses: $$P = 2(2x + 2)$$ Factor out 2: $$P = 2 \times 2(x + 1) = 4(x + 1)$$ 4. **Step b) Find the perimeter when $x = 5$:** Substitute $x = 5$ into the expression: $$P = 4(5 + 1) = 4 \times 6 = 24$$ 5. **Answer:** a) The perimeter expression is $P = 4(x + 1)$. b) When $x = 5$, the perimeter is $24$ units. This completes the solution for problem 22.