Practical Examples of Linear Inequalities in Daily Life for Students

📚 Quick Study Guide

• 🔢 Linear inequalities involve comparing two expressions using inequality symbols like $<$, $>$, $\leq$, or $\geq$.
• 🛍️ They often model situations where there's a minimum or maximum limit.
• ⚖️ Solving linear inequalities is similar to solving equations, but multiplying or dividing by a negative number reverses the inequality sign.
• графи The solution to a linear inequality can be represented graphically on a number line.
• 💡 Real-world problems involving budgets, time constraints, and resource allocation frequently use linear inequalities.

Practice Quiz

1. A student needs at least 80 points on the final exam to get an A in the course. If their current average is 75, which inequality represents the score, $x$, they need on the final?
   1. $x + 75 \geq 80$
   2. $x + 75 > 80$
   3. $x \geq 5$
   4. $x \geq 80$
2. A phone plan costs $20 per month plus $0.10 per text message. If you want to spend no more than $35 per month, what is the maximum number of text messages, $t$, you can send?
   1. $0.10t + 20 \leq 35$
   2. $0.10t + 20 \geq 35$
   3. $0.10t \leq 35$
   4. $20t + 0.10 \leq 35$
3. A bakery needs to make at least 50 cupcakes for an event. They've already made 24. Which inequality represents how many more cupcakes, $c$, they need to bake?
   1. $c + 24 \geq 50$
   2. $c + 24 \leq 50$
   3. $c \geq 26$
   4. $c \leq 26$
4. You want to buy some songs online. Each song costs $1.29. If you have $10, what is the maximum number of songs, $s$, you can buy?
   1. $1.29s \leq 10$
   2. $1.29s \geq 10$
   3. $s \leq 10$
   4. $s \geq 1.29$
5. A store sells apples for $2 each and bananas for $1 each. You want to spend no more than $10. If you buy 3 apples, which inequality represents the number of bananas, $b$, you can buy?
   1. $2(3) + b \leq 10$
   2. $2(3) + b \geq 10$
   3. $2 + b \leq 10$
   4. $3 + b \leq 10$
6. A taxi charges $3 initially plus $2 per mile. If you want to spend no more than $15, what is the maximum number of miles, $m$, you can travel?
   1. $2m + 3 \leq 15$
   2. $2m + 3 \geq 15$
   3. $2m \leq 15$
   4. $3m + 2 \leq 15$
7. A community center needs to raise at least $5000 for a new program. They have already raised $2700. Which inequality represents the amount of money, $m$, they still need to raise?
   1. $m + 2700 \geq 5000$
   2. $m + 2700 \leq 5000$
   3. $m \geq 2300$
   4. $m \leq 2300$