Inequalities in One Variable
10-3Solving Problems Involving Inequalities
Overview
Translate words to inequalities: ‘at most’ → ≤, ‘at least’ → ≥, ‘more than’ → >, ‘less than’ → <.
Key ideas
- Identify the boundary value and direction.
- Set up and solve the inequality.
- Interpret the answer in context.
Worked examples
Example 1
Problem. A car rental costs $30 plus $0.20/mi. With $50, how many miles?
Solution. 30 + 0.2m ≤ 50 → m ≤ 100.
Practice
Try each one. Click Show answer when ready.
- 1.
5 more than twice n is at least 17.
- 2.
Triple a number is less than 24.
- 3.
Sum of x and 4 is at most 10.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Three times a number minus 5 is at least 16. What is the number?
- 2.
A student needs an average of at least 80 on 4 tests. Scores so far: 78, 82, 75. What is needed on the fourth test?