1. **State the problem:** Dario added $x$ songs and Kareem added $y$ songs to a shared playlist. Each song is assumed to be 3.5 minutes long on average. The total playlist length is at least 120 minutes. 2. **Write the inequality:** The total length of the playlist is the sum of the lengths of all songs added by Dario and Kareem. 3. **Formula:** Total length $= 3.5x + 3.5y$ 4. **Inequality for at least 120 minutes:** $$3.5x + 3.5y \geq 120$$ 5. **Simplify the inequality by factoring out 3.5:** $$3.5(x + y) \geq 120$$ 6. **Divide both sides by 3.5 to isolate $x + y$:** $$\frac{\cancel{3.5}(x + y)}{\cancel{3.5}} \geq \frac{120}{3.5}$$ 7. **Calculate the division:** $$x + y \geq \frac{120}{3.5} = 34.2857$$ 8. **Final inequality:** $$x + y \geq 34.29$$ This means the total number of songs added by Dario and Kareem must be at least approximately 34.29 to have a playlist length of at least 120 minutes. **Answer:** $$3.5x + 3.5y \geq 120$$