1. **State the problem:** Caitlan has 50 to spend on canoeing. She must pay an 18 deposit plus 10.5 per hour. We want to find the greatest number of hours $x$ she can rent the canoe. 2. **Write the inequality:** The total cost is deposit plus hourly cost, so $$18 + 10.5x \leq 50$$ 3. **Isolate the variable term:** Subtract 18 from both sides: $$18 + 10.5x - 18 \leq 50 - 18$$ $$\cancel{18} + 10.5x - \cancel{18} \leq 32$$ $$10.5x \leq 32$$ 4. **Solve for $x$:** Divide both sides by 10.5: $$\frac{10.5x}{10.5} \leq \frac{32}{10.5}$$ $$\cancel{10.5}x \leq \frac{32}{10.5}$$ $$x \leq 3.0476...$$ 5. **Interpret the result:** Caitlan can rent the canoe for up to about 3.05 hours. Since she likely rents by whole hours, the greatest whole number of hours is 3. **Final answer:** $$x \leq 3$$