Real-world examples of solutions to inequalities

📚 Quick Study Guide

🔢 Definition: An inequality is a mathematical statement that compares two expressions using symbols like $<$, $>$, $\leq$, or $\geq$. ⚖️ Solving Inequalities: Similar to solving equations, but multiplying or dividing by a negative number reverses the inequality sign. 📈 Graphing Inequalities: Inequalities can be represented on a number line or a coordinate plane. 🚧 Interval Notation: A way to represent a set of numbers using intervals, e.g., $(a, b)$, $[a, b]$, $(a, \infty)$. 💡 Key Principle: Remember to flip the inequality sign when multiplying or dividing by a negative number.

Practice Quiz

1. Question 1: A phone plan costs $20 per month plus $0.10 per text message. You want to spend no more than $30 per month. What is the maximum number of text messages you can send?
   1. 50
   2. 100
   3. 150
   4. 200
2. Question 2: You need to score at least 80 points on your final exam to get an A in the class. The exam is worth 200 points. What percentage do you need to score?
   1. 20%
   2. 40%
   3. 60%
   4. 80%
3. Question 3: A store is having a sale where all items are 25% off. You have $50 to spend. What is the maximum original price of an item you can buy?
   1. $50
   2. $66.67
   3. $75
   4. $100
4. Question 4: The temperature must be between 60°F and 80°F for an outdoor event. Which inequality represents this situation, where $T$ is the temperature?
   1. $60 < T < 80$
   2. $60 > T > 80$
   3. $60 \leq T \leq 80$
   4. $T < 60 \text{ or } T > 80$
5. Question 5: A rectangle has a width of 5 cm. What must the length be to ensure the area is greater than 30 cm²?
   1. Length > 5 cm
   2. Length > 6 cm
   3. Length < 5 cm
   4. Length < 6 cm
6. Question 6: You are saving money for a $500 computer. You already have $200 saved. If you save $20 per week, how many weeks will it take to save enough money?
   1. 10 weeks
   2. 15 weeks
   3. 20 weeks
   4. 25 weeks
7. Question 7: A taxi charges $3 initially plus $2 per mile. How far can you travel if you have $15?
   1. 5 miles
   2. 6 miles
   3. 7 miles
   4. 8 miles