1. **State the problem:** We are given a rectangular prism with surface area 290 in², and dimensions including edges 11 in, 3 in, and an unknown edge $x$. We need to find $x$. 2. **Recall the formula for surface area of a rectangular prism:** $$SA = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height. 3. **Assign the given dimensions:** Let $l = 11$, $h = 3$, and $w = x$ (the unknown). 4. **Write the surface area equation:** $$290 = 2(11 \times x + 11 \times 3 + x \times 3)$$ 5. **Simplify inside the parentheses:** $$290 = 2(11x + 33 + 3x)$$ $$290 = 2(14x + 33)$$ 6. **Distribute the 2:** $$290 = 28x + 66$$ 7. **Isolate $x$:** $$290 - 66 = 28x$$ $$224 = 28x$$ 8. **Divide both sides by 28:** $$\cancel{28}x = \frac{224}{\cancel{28}}$$ $$x = 8$$ **Final answer:** $$x = 8$$ inches