1. **State the problem:** Ignacio's legs start at 49.3 cm from the floor, and the desk bottom is at 74.5 cm. Each clockwise rotation raises his legs by 4.8 cm. We want to find the number of rotations $r$ so that his legs do not touch the desk, meaning the height after rotations must be less than or equal to 74.5 cm. 2. **Write the inequality:** The initial leg height plus the increase per rotation times the number of rotations must be less than or equal to the desk height: $$49.3 + 4.8r \leq 74.5$$ 3. **Solve the inequality:** Subtract 49.3 from both sides: $$4.8r \leq 74.5 - 49.3$$ $$4.8r \leq 25.2$$ Divide both sides by 4.8: $$r \leq \frac{25.2}{4.8}$$ $$r \leq 5.25$$ 4. **Interpret the solution:** Since $r$ represents the number of rotations, it must be a whole number less than or equal to 5.25, so Ignacio can make up to 5 full clockwise rotations without his legs touching the desk. **Final answer:** $$r \leq 5.25$$ or in whole rotations, $$r \leq 5$$