1. **State the problem:** Find the weight of Kiran's backpack given that it weighs 3 1/2 pounds less than Clare's backpack, which weighs 14 3/4 pounds. 2. **Identify the correct equations:** - $x + 3 \frac{1}{2} = 14 \frac{3}{4}$ (Kiran's weight plus 3 1/2 equals Clare's weight) - $x = 14 \frac{3}{4} - 3 \frac{1}{2}$ (Kiran's weight equals Clare's weight minus 3 1/2) The other equations are incorrect for this situation. 3. **Convert mixed numbers to improper fractions:** - $3 \frac{1}{2} = \frac{7}{2}$ - $14 \frac{3}{4} = \frac{59}{4}$ 4. **Set up the equation:** $$x + \frac{7}{2} = \frac{59}{4}$$ 5. **Solve for $x$ by subtracting $\frac{7}{2}$ from both sides:** $$x = \frac{59}{4} - \frac{7}{2}$$ 6. **Find common denominator and subtract:** $$x = \frac{59}{4} - \frac{14}{4} = \frac{59 - 14}{4} = \frac{45}{4}$$ 7. **Convert back to mixed number:** $$x = 11 \frac{1}{4}$$ **Answer:** Kiran's backpack weighs $11 \frac{1}{4}$ pounds.