1. **State the problem:** Diane wants to rent a truck and compare costs between two companies. Company A charges a flat fee of 121. Company B charges 65 plus 0.70 per mile driven. We want to find for which mileages $m$ Company A is cheaper than Company B. 2. **Set up the inequality:** Company A cost $<$ Company B cost $$121 < 65 + 0.70m$$ 3. **Solve the inequality:** Subtract 65 from both sides: $$121 - 65 < 65 + 0.70m - 65$$ $$56 < 0.70m$$ Write the step with cancellation to show division: $$\cancel{56} < \cancel{0.70}m$$ Divide both sides by 0.70: $$\frac{56}{0.70} < m$$ Calculate the division: $$80 < m$$ 4. **Interpret the solution:** Diane should choose Company A if she drives more than 80 miles. **Final answer:** $$m > 80$$