[Video Placeholder - Introduction to inequality word problems]
Duration: 5:20
Linear inequalities appear in real-world situations where quantities have minimum or maximum limits rather than exact values. Key differences from equations:
Maria has $100 to spend on books and movies. Books cost $12 each and movies cost $8 each. She wants to buy at least 5 movies. Write and graph a system of inequalities to represent this situation.
To pass his math class, Jason needs an average of at least 70 on four tests. His first three test scores are 65, 72, and 68. What score does he need on the fourth test to pass?
A parking garage charges $3 for the first hour and $2 for each additional hour or part thereof. You have $15 for parking. Write an inequality to represent how many hours you can park.
Step 1: Define variable
Let h =
Step 2: Write the inequality
Step 3: What is the maximum whole number of hours?
| Word Phrase | Inequality Symbol |
|---|---|
| At least, no less than | ≥ |
| At most, no more than | ≤ |
| More than, above | > |
| Less than, below | < |
The student council needs to raise at least $500 for a charity. They've raised $175 so far. If each cookie they sell raises $1.50, how many more cookies do they need to sell?
A phone plan includes 500 minutes for $30, with each additional minute costing $0.10. You want to spend no more than $40 this month. Which inequality represents the maximum additional minutes (m) you can use?