1. **State the problem:** Samantha has 1500 in her bank account and spends 35 per week. We want to find how many weeks, $x$, it will take for her account balance to be less than 915. 2. **Write the inequality:** The amount left after $x$ weeks is $1500 - 35x$. We want this to be less than 915, so the inequality is: $$1500 - 35x < 915$$ 3. **Solve the inequality:** Subtract 1500 from both sides: $$1500 - 35x - 1500 < 915 - 1500$$ $$-35x < -585$$ 4. **Divide both sides by -35:** Remember, dividing by a negative number reverses the inequality sign. $$\cancel{-35}x > \cancel{-35} \frac{-585}{-35}$$ $$x > \frac{585}{35}$$ 5. **Simplify the fraction:** $$x > 16.7142857...$$ 6. **Interpret the result:** Samantha will have less than 915 in her account after more than approximately 16.7 weeks. 7. **Round to the nearest whole number:** $$x > 17$$ **Final answer:** - Inequality: $$1500 - 35x < 915$$ - Number of weeks: 17 Samantha will have less than 915 in her account after 17 weeks.